Chemical KineticsMoving Charges and MagnetismMicrobes in Human WelfareSemiconductor Electronics: Materials, Devices and Simple Circuits. 2. Then, one ace can be selected in 4 C 1 ways and the remaining 4 cards can be selected out of the 4 8 cards in 4 8 C 4 ways. Solution. Thus there are 10 possible high cards. Therefore, we can derive the combinations formula from the permutations formula by dividing the number of permutations (5! / 2!) by 3! to obtain 5! / (2! * 3!) = 10 different ways. Number of cards in a deck=52Number of queens drawn=2Number of queens present in a deck=4. Playing Cards: From a standard deck of 52 cards, in how many ways can 7 cards be drawn? 2. It may take a while to generate large number of combinations. In a deck of 5 2 cards, there are 4 aces. The answer is \(\binom{52}{5}\). In This Article. To refer to the number of cards drawn, I will add the number at the end of the name, for example, If I want to tell the frequency of two pairs in a 5-card hand, I will say 2K2K5. Your $\dfrac{52!}{47!}$ is the number of ways to deal $5$ cards: it counts each of the $5!=120$ possible dealing orders of a given hand separately. Class 10. View Solution. This is the total number of arrangements of 2 Aces of the 4 in A. Following this logic, I tried to calculate the probability of getting two pair. In 5-Card combinations, you would have 4 possible royal flushes. You can also convert the probability into a percentage by multiplying it by 100. An Introduction to Thermal PhysicsDaniel V. To convert the number of combinations or permutations into a probability of drawing a specific results, divide one by the result of your calculation. Combinatorial calculator - calculates the number of options (combinations, variations. In a pack of 52 cards , there are four aces. Determine the number of 5 cards combination out of a deck of 52 cards if at least one of the cards has to be a king. 5 card poker hand combination a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter n P r = n!/r!(n - r)! factorial The product of an integer and all the integers below it probability the likelihood of an event happening. In this case, you are looking for a permutation of the number of ways to order 5 cards from a set of 52 objects. Then the solution to the problem - that is, the probability of at least one ace appearing in a 5-card hand - is one minus the complement:Thus we use combinations to compute the possible number of 5-card hands, (_{52} C_{5}). 7k points) permutations and combinations; class-11 +4 votes. How many possible 5 card hands from a standard 52 card deck would consist of the following cards? (a) two clubs and three non-clubs (b) four face cards and one non-face card (c) three red cards, one club, and one spade (a) There are five-card hands consisting of two clubs and three non-clubs. asked Apr 30, 2020 in Permutations and Combinations by PritiKumari ( 49. by Maths experts to help you in doubts & scoring excellent marks in Class 11 exams. I developed a simulator Texas hold'em and during this development I found the number of 7462 unique combinations (52 - 5/5 cards) on the flop. The 5 cards of the hand are all distinct, and the order of cards in the hand does not matter so it is a combinatorial problem. 1-on-1 Online Tutoring. Therefore, to calculate the number of combinations of 3 people (or letters) from a set of six, you need to divide 6!. We have yet to compute the number of arrangements of the remaining cards. Question 5: Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls, and 7 blue. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. ,89; 3. Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king? Advertisement. Q. A combination of 5 cards have to be made in which there is exactly one ace. Mathematics Combination with Restrictions Determine the. No. ∴ No. And so on. Unit 7 Probability. If you want to count the size of the complement set and. ”. of ways of selecting 4 cards from the remaining deck of 48 cards = ⁴⁸C₄. That $4$ appears in the Frequency column. Calculate Combinations and Permutations in Five Easy Steps: 1. A combination of 5 cards have to be made in which there is exactly one ace. A card is selected from a standard deck of 52 playing cards. If more than one player remains after that first. 2: The Binomial Theorem. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, is. So there are (26 C 5) = 26! ⁄ 5!(26−5)! = 26! ⁄ 5!21!Determine whether the object is a permutation or a combination. royal flush straight flush four of a kind full house flush straight (including a straight flush and a royal flush) three of a kind one pair neither a repeated. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Let’s enter these numbers into the equation: 69 C 5 = 11,238,513. The number of combinations n=10, k=4 is 210 - calculation result using a combinatorial calculator. View solution > A man has of selecting 4 cards from an ordinary pack of playing cards so that exactly 3 of them are of the same denominations. Solution : Total number of cards in a. View Solution. Thus, the number of combinations is:asked Sep 5, 2018 in Mathematics by Sagarmatha (55. West gets 13 of those cards. No. 5 card poker hand combination a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter n P r = n!/r!(n - r)! factorial The product of an integer and all the integers below it probability the likelihood of an event happening. Step by step video, text & image solution for Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Then multiply the two numbers that add to the total of items together. Click here👆to get an answer to your question ️ "Determine the number of 5 - card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. How many ordered samples of 5 cards can be drawn from a deck of 52. Create Tests & Flashcards. Player 2's Best Hand is: K K Q Q J J 8 8 5 5. A combination of 5 cards have to be made in which there is exactly one ace. The total number of combinations would be 2^7 = 128. This value is always. The expression you are. Order doesn't matter, because A,2,3,4,5 is the same hand has 3,4,2,A,5. Unit 3 Summarizing quantitative data. 1. , A = {1, 2, 3,. Find the probability of being dealt a full house (three of one kind and two of another kind). You are dealt a hand of five cards from a standard deck of 52 playing cards. 00196 To find the probability, we need to find the fraction where the numerator is the number of ways to have a flush and the. The following exercises deal with our version of the game blackjack. 05:01. Even if we had. Where, n is the total number in the dataset. (For those unfamiliar with playing cards, here is a short description. 1 Expert Answer. View Solution. All we care is which five cards can be found in a hand. number of ways selecting one ace from 4 aces = ⁴C₁ number of ways selecting 4 cards from 48 cards = ⁴⁸C₄ now, A/C to concept of fundamental principle of counting, 5 cards with exactly one ace can be selected in ⁴C₁ × ⁴⁸C₄ ways. The simplest explanation might be the following: there are ${52}\choose{4}$ possible combinations of 4 cards in a deck of 52. A 4-card hand is drawn from a standard deck of 52 cards. A royal flush is defined as an ace-high straight flush. The 7 th term of ( )2x − 1 n is 112x2. Number of hands containing at least one black card=2,598,960-67,780=2,531,180. What is the probability that the number on the ball is divisible by 2 or 3. 6! 3! = 6 · 5 · 4 · 3! 3! = 6 · 5 · 4 = 120. Once everyone has paid the ante or the blinds, each player receives five cards face down. Win the pot if everyone else folds or if you have the best hand. In a deck of 52 cards, there are 4 aces. There are total 4 King. By multiplication principle, the required number of 5 card combinations are. 448 c. Thus the number of ways of selecting the cards is the combination of 48 cards taken 4 at a time. Verified by Toppr. For example, 3! = 3 * 2 * 1 = 6. Combination; 8 6) There are 15 applicants for two Manager positions. In a pack of 52 cards , there are four aces. ". A poker hand consists of 5 cards from a standard deck of 52. Open in App. Each of these 2,598,960 hands is equally likely. 2 Answers Lotusbluete Feb 2, 2016 There are #10# possible #5#-card hands with exactly #3# kings and exactly #2# aces. combination for m and coins {a,b} (without coin c). Then you add 0000, which makes it 10,000. Join / Login. Then, one ace can be selected in 4C1 ways and the remaining 4 cards can be selected out of the 48 cards in 48C4 ways. Here are the steps to follow when using this combination formula calculator: On the left side, enter the values for the Number of Objects (n) and the Sample Size (r). Determine the value of x that satisfies the value of the square number below 24x+14 = 64x+2. In other words, for a full house P =. Find how many combinations of : 3 cards of equal face values and 2 cards of different values. c. To calculate how many 5 card hands contain at least one black card it is easier to calculate how manny hands have no black cards and the subtract this from the total number of 5 card hands. There are 4 kings in the deck of cards. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. . 98 you can get a salad, main course, and dessert at the cafeteria. 4. C. According to wikipedia, there are 134,459 distinct 5 card. 2. of ways of selecting remaining 4 cards from remaining 48 cards = . a 10-digit telephone number (including area code) This is neither a permutation nor a combination because repetition is allowed. There are also two types of combinations (remember the order does not matter now): Repetition is Allowed: such as coins in your pocket (5,5,5,10,10) No Repetition: such as lottery numbers (2,14,15,27,30,33) 1. A straight flush is completely determined once the smallest card in the straight flush is known. ) ID Cards How many different ID cards can be made if there are 6 6 digits on a card and no digit. In poker one is dealt five cards and certain combinations of cards are deemed valuable. ". The number of ways this may be done is 6 × 5 × 4 = 120. Ex 6. 3 2 6 8. 4 cards from the remaining 48 cards are selected in ways. . Seven points are marked on a circle. (Total 5-card combinations) = [(C(13, 5) * 4) – (10 * 4)] / C(52, 5) This probability, though involving some calculations, is approximately 0. However, since suits are interchangeable in poker, many of these are equivalent - the hand 2H 2C 3H 3S 4D is equivalent to 2D 2S 3D 3C 4H - simply swap the suits around. 2. I am given a deck of 52 cards in which I have to select 5 card which. - 27! is the number of ways the remaining 36 - 9 = 27 cards can be arranged. Author: Jay Abramson. Subtract the numerator (5) from the denominator (13) : 13 - 5 = 8 . Alternatively, this is asking for the number of ways to leave behind 47 (52-5) cards in a particular order from the deck box. Ways of selecting a king from the deck = 4 C 1. (e. Since there are 52 cards in a deck and the order of cards doesn’t matter, the sample space for this experiment has 52 C 5 = 2,598, 960 52 C 5 = 2,598,960 possible 5-card hands. Determine the number of 5 -card combination out of a deck of 52 cards if each selection of 5 cards has exactly one king. Determine the number of 5 card combinations out of a deck of 52 cards if . Thus, by multiplication principle, required number of 5 card combinations. Solve Study Textbooks Guides. So you want to stick with $4^5*10$ in your numerator. 7) How many ways can the positions of president and vice president be assigned from a group of 8 people? 8) Find the Number of hugs possible in a family of 5 people (no repeat hugs). The probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand by the total number of 5-card hands (the sample space, five-card hands). Hence, there are 2,598,960 distinct poker hands. (485) (525), ( 48 5) ( 52 5), for we have 48 choose 5 possible hands with no aces. asked Sep 10, 2019 in Mathematics by Vamshika ( 70. Solution. This includes all five cards. Solve Study Textbooks Guides. The State of Climate Action 2023 provides the world’s most comprehensive roadmap of how to close the gap in climate action across sectors to limit global warming. 05:26. Explanation: To determine the number of ways to choose 5 cards out of a deck of 52 cards, we can use the concept of combinations. does not matter, the number of five card hands is: 24. In a deck of 52 cards, there are 4 aces. n = the total number of objects you are choo sing from r = the number of objects you are choosing Order doesn't matter, total number of ways to choose differen t objects out of a total of when order do esn't matter. Determine the number of 5 card combinations out of a deck of 5 2 cards if there is exactly one ace in each combination. Five-Card Draw Basics. = 48C4 ×4 C1. 2. We may be compensated when you click on product links, such as credit cards, from one or more of our advertising partners. This probability is. A combination of 5 cards is to be selected containing exactly one ace. Q5. Each card may be of four different suits. The 11 Best Credit Card Combinations – Amex, Chase, Citi, Capital One [November 2023] Stephen Au Updated: November 14, 2023, 9:35am CST. Selection of 5 cards having at least one king can be made as follows: 1 king and 4 non kings or 2 kings and 3 non - j8li3muee. 5) Selecting which seven players will be in the batting order on a 8 person team. . Solution: From a deck of 52 cards, 5-card combinations have to be made in such a way that in each selection of 5 cards, there is exactly one king. The index part added ensures the hash will remain unique. 4 cards out of the remaining 48 cards can be selected in `""^48C_4` ways. ⇒ C 1 4 × C 4 48. Number of ways to answer the questions : = 7 C 3 = 35. Determine the number of 5 -card combination out of a deck of 52 cards if each selection of 5 cards has exactly one king. . Answer and. The easiest answer is to find the probability of getting no n o aces in a 5-card hand. $$mathsf P(Kleq 3) = 1 -mathsf P(K=4)$$ The probability that you will have exactly all four kings is the count of ways to select 4 kings and 1 other card divided by the count of ways to select any 5 cards. Join / Login. If 52 cards, there are 4 aces and 48 other cards, (∵ 4 + 48 = 52). asked Dec 30, 2016 in Mathematics by sforrest072 ( 130k points) permutations and combinations In a deck, there is 4 ace out of 52 cards. Therefore, the number of possible poker hands is \[\binom{52}{5}=2,598,960. a) Four cards are dealt, one at a time, off the top of a well-shuffled deck. Selection of 5 cards having at least one king can be made as follows: 1 king and 4 non kings or 2 kings and 3 non kings or 3 kings and 2 non kings or 4 kings and 1 non king. Divide the latter by the former. Enter the total number of objects (n) and the number of elements taken at a time (r) 3. It may take a while to generate large number of combinations. This is a combination problem. Hence, the number of 5 card combinations out of a deck of 52 cards is 778320. How many possible 5-card hands from a standard 52-card deck would consist of the following cards? (a) two spades and three non-spades (b) four face. 20%. Solve Study Textbooks Guides. Click here👆to get an answer to your question ️ Determine the number of 5 - card combination out of a deck of 52 cards if each selection of 5 cards has exactly one king. Then, one ace can be selected in (^4C_1) ways and the remaining 4 cards can be selected out of the 48 cards in (^{48}C_4) ways. Determine the number of 5 card combinations out of a deck of 52 cards if ther is exactly one ace in each combination. Whether you use a hand calculator or a computer you should get the number: [Math Processing Error] 1365. Since, there is exactly one ace in a combination of 5 cards, so no of ways of selecting one ace = . 5 6 4 7. Solution Show Solution. Determine the number of 5 card combination out of a deck of 5 2 cards if each selection of 5 cards has at least one king. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly three aces in each combination. Four of a kind c. Find how many combinations of : 3 cards of equal face values and 2 cards of different values. Step by step video, text & image solution for Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. After the first card, the numbers showing on the remaining four cards are completely determine. (A poker hans consists of $5$ cards dealt in any order. By fundamental principle of counting, The required number of ways = ⁴C₁ × ⁴⁸C₄ = (4!) / [1!STEP 2 : Finding the number of ways in which 5 card combinations can be selected. Our ncr calculator uses this formula for the accurate & speedy calculations of all the elements of. In that 5 cards number of aces needed = 3 . Solve Study Textbooks Guides. We may be compensated when you click on product links, such as credit cards, from one or more of our advertising partners. There are 52 13 = 39 cards that North does not hold. Medium. If you want to count the size of the complement set and subtract off from ${52 choose 5}$, then you need to find the number of five card poker hands which contain one or more cards of another suite. Total number of cards to be selected = 5 (among which 1 (ace) is already selected). Find the probability of getting an ace. Class 7. Medium. For example, a king-high straight flush would be (13-13)*4+5 = 5. 1. means the number of high card hands is 2598960 – 40 – 624 – 3744 – 5108 – 10200 – 54912 – 123552 – 1098240 = 1,302,540. Counting numbers are to be formed using only the digits 6, 4, 1, 3, and 5. The total number of combinations of A and B would be 2 * 2 = 4, which can be represented as: A B. Determine the number of five-card poker hands that can be dealt from a deck of 52 cards. 1 answer. One card is selected from a deck of playing cards. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Click here👆to get an answer to your question ️ "the strip. If we use the combinations formula, we get the same result. Class 5. A combination of 5 cards have to be made in which there is exactly one ace. Q. For example, a “four of a kind” consists of four cards of the same value and a fifth card of arbitrary. CBSE Board. We are using the principle that N (5 card hands)=N. P (10,3) = 720. So the number of five-card hands combinations is:. There are 13 values you can select for the four of a kind: ${13 choose 1}$ The fifth can be any of the 52 - 4 remaining cards: ${52 - 4 choose 1}$For each condition, you can have two possibilities: True or False. View Solution. To find the number of full house choices, first pick three out of the 5 cards. There are 10 possible 5-card hands with exactly 3 kings and exactly 2 aces. difference between your two methods is about "how" you select your cards. GRE On-Demand. Exactly 1 ace out of 4 aces can be selected in ⁴C₁ ways. For example, we can take out any combination of 2 cards. Part a) is effectively asking, given these 39 cards how many ways are there of choosing 5 in other words what is 39 choose 5: $$inom{39}{5}=575757$$ For part b) we can do something similar, lets start with choosing 1 club. Things You Should Know. Second method: 4 digits means each digit can contain 0-9 (10 combinations). asked Sep 6, 2018 in Mathematics by Sagarmatha (55. For the second rank we choose 2 suits out of 4, which can be done in (4 2) ( 4 2) ways. The equation you provided is correct in the sense that it tells us how many ways we can select 4 ace's out of 5 cards that are selected at once out of the total possible 5 card. Now if you are going to pick a subset r out of the total number of objects n, like drawing 5 cards from a deck of 52, then a counting process can tell you the number of different ways you can. Dealing a 5 card hand with exactly 1 pair. Determine the number of 5 card combinations out of a deck of 52 cards, if there is exactly one ace in each combination. Edited by: Juan Ruiz. 4 5 1 2. Let’s begin with an example in which we’ll calculate the number of [Math Processing Error] 3 -combinations of ten objects (or in this case, people). 13 clubs:To determine the number of combinations, simply divide the number of permutations by the factorial of the size of the subset. Verified by Toppr. Transcript. From a deck of 52 cards, 5 cards combination is taken out Find the number of combinations at which the combination has at least one ace. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. You are "duplicating combinations", because the same king that you choose out of 4 4 kings in one combination, can be chosen out of 51 51 cards in another combination. Combination; 105 7) You are setting the combination on a five-digit lock. asked Dec 30, 2016 in Mathematics by sforrest072 (130k points) permutations and combinations; combinations; 0. For the purpose of this table, a royal flush, straight flush, flush, and straight must use all cards. This value is always. 3 2 6 8. The first digit has 10 combinations, the second 10, the third 10, the fourth 10. (52 5)!5! = 2598960 di erent ways to choose 5 cards from the available 52 cards. Ask doubt. Verified by Toppr. There are 52 5 = 2,598,9604 possible poker hands. (r + n -1)! r! × (n - 1)! This free calculator can compute the number of possible permutations and. Determine the number of 5 card combinations out of a deck of 52 cards, if there is exactly one ace in each combination. The total number of 5-card poker hands is . 3. The solution (this is an example) is stated as: The number of different poker hands is (525) ( 52 5). For many experiments, that method just isn’t practical. Created January 11, 2019 3:11pm UTC. The formula for the. The number of ways to arrange five cards of four different suits is 4 5 = 1024. n C r = n! ⁄ r! (n-r)! ,0 < r ≤n. This is a combination problem. Establish your blinds or antes, deal 5 cards to each player, then bet. Find the number of 5 card combination out of a deck of 52 cards if there is exactly one ace in each combination. out of 4 kings in one combination, can be chosen out of 51 cards in. Solve. If more than one player has a flush you award the pot to the player with the highest-value flush card. e. 17. The exclamation mark (!) represents a factorial. Thus, by multiplication principle, required number of 5 card combinations 5 card poker hand combination a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter n P r = n!/r!(n - r)! factorial The product of an integer and all the integers below it probability the likelihood of an event happening. An example is 9♥, 8♣, 7♠, 6♦, 5♥. Example 2: If you play a standard bingo game (numbers from 1 to 75) and you have 25 players (25 cards), and if you play 30 random values, you will get an average of 3 winning lines. Combinations sound simpler than permutations, and they are. Next subtract 4 from 1024 for the four ways to form a flush, resulting in a straight flush, leaving 1020. The number of ways in which 5 hand cards are arranged is $ 2, 598, 960 $. Unit 6 Study design. _square]. Solution. 6 Determine the number of 5 card combinations out of a deck of 52 cards if there is. Previous Question < > Next. Determine the number of 4 card combinations out of a deck of 52 cards if there is no ace in each combination. A researcher selects. Then, one ace can be selected in ways and other 4 cards can be selected in ways. A combination of 5 cards have to be made in which there is exactly one ace. The formula is: C(n, r) = n! / (r!(n-r)!) where n is the total number of. F F. Each group of three can be arranged in six different ways 3! = 3 ∗ 2 = 6, so each distinct group of three is counted six times. There are 52 - 4 = 48 non-kings to select the remaining 4 cards. And how many ways are there of drawing five cards in general? $endgroup$ – joeb. 10,000 combinations. If you are dealt two kings, it does not matter if the two kings came with the first two cards or the last two cards. CBSE Board. Here is a table summarizing the number of 5-card poker hands. Then, one ace can be selected in 4C1ways and the remaining 4 cards can be selected out of the 48cards in 48 C4 ways. . So your approach would be $52$ (choose the first card of the pair) times $3$ (choose the second card of the pair) times 48 (choose the third card-can't match the. This video explains how to determine the probability of a specific 5 card hand of playing cards. four of the same suit. number of ways selecting one ace from 4 aces = ⁴C₁ number of ways selecting 4 cards from 48 cards = ⁴⁸C₄ now, A/C to concept of fundamental principle of counting, 5 cards with exactly one. Insert the numbers in place of variables in your formula and calculate the result. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. If we pick 5 cards from a 52 card deck without replacement and the same two sets of 5 cards, but in different orders, are considered different, how many sets of 5 cards are there? Solution. In a deck of 52 cards, there are 4 kings. How many ways are there to select 47 cards from a deck of 52 cards? The different ways to select 47cards from 52 is. Hence, using the multiplication principle, required the number of 5 card combination It's equivalent to figuring out how many ways to choose 2 cards from a hand of 4 kings (king, king, king, king) to turn into aces; it's simply ₄C₂. Paired hands: Find the number of available cards. The number of arrangement of both two 'A' and two 'R' together can be found by taking a group of two 'A' as one and two 'R' as another entity. SEE MORE TEXTBOOKS. Solve Study Textbooks Guides. mathematics permutations and combinations word problem find the number of combinations. There are $4;;Ace$ cards in a deck of $52;;cards. Earning rates: 3X points on restaurants, gas stations, supermarkets, air travel and hotels; 2X points on. Combination: Choosing 3 desserts from a menu of 10. Take 3 letters a, b, and c. A combination of 5 cards have to be made in which there is exactly one ace. Selection of 5 cards having at least one king can be made as follows: 1 king and 4 non kings or 2 kings and 3 non kings or 3 kings and 2 non kings or 4 kings and 1 non king. Solution. of cards in a deck of cards = 52. Determine the number of different possibilities for two-digit numbers. , 10, J, Q, K). If you have fewer cards, you will likely need to draw more numbers to get the same number of winning lines as the probabilities are lower for a player to get a bingo. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Click here👆to get an answer to your question ️ Determine the number of 5 card combinations out of a deck of 52 cards if there 1s exactly one ace in each combination. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. Since there are $5!$ orderings, the number of ways to get dealt an A-thru-5 straight, in any order, but counting different orderings as distinct, is $5! 4^5$. The other way is to manually derive this number by realizing that to make a high card hand the hand must consist of all five cards being unpaired, non-sequential in rank, and not all of the same suit. Example [Math Processing Error] 3. It's got me stumped for the moment.