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Probability with the Question 13, 11.5.15 HW Score: 46.03%,9.67 of 21 Part 1 of 3 points Points: 0 of 1 Save Question list -nuvu..... Question 12 Question 13 Question 14 Question 15 A hand consists of 5 cards from a well-shuffled deck of 52 cards. a. Find the total number of possible 5 -card poker hands. b. A heart flush is a 5 -card hand consisting of all heart cards. Find the number of possible heart flushes. c. Find the probability of being dealt a heart flush. a. There are a total of ◻ poker hands.

Probability with the\newlineQuestion 1313, 1111.55.1515\newlineHW Score: 46.03%,9.67 46.03 \%, 9.67 of 2121\newlinePart 11 of 33\newlinepoints\newlinePoints: 00 of 11\newlineSave\newlineQuestion list\newline-nuvu.....\newlineQuestion 1212\newlineQuestion 1313\newlineQuestion 1414\newlineQuestion 1515\newlineA hand consists of 55 cards from a well-shuffled deck of 5252 cards.\newlinea. Find the total number of possible 55 -card poker hands.\newlineb. A heart flush is a 55 -card hand consisting of all heart cards. Find the number of possible heart flushes.\newlinec. Find the probability of being dealt a heart flush.\newlinea. There are a total of □ \square poker hands.

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Q. Probability with the\newlineQuestion 1313, 1111.55.1515\newlineHW Score: 46.03%,9.67 46.03 \%, 9.67 of 2121\newlinePart 11 of 33\newlinepoints\newlinePoints: 00 of 11\newlineSave\newlineQuestion list\newline-nuvu.....\newlineQuestion 1212\newlineQuestion 1313\newlineQuestion 1414\newlineQuestion 1515\newlineA hand consists of 55 cards from a well-shuffled deck of 5252 cards.\newlinea. Find the total number of possible 55 -card poker hands.\newlineb. A heart flush is a 55 -card hand consisting of all heart cards. Find the number of possible heart flushes.\newlinec. Find the probability of being dealt a heart flush.\newlinea. There are a total of □ \square poker hands.
  1. Calculate Total Poker Hands: To find the total number of possible 55-card poker hands, we use the combination formula which is C(n,k)=n!k!(n−k)!C(n, k) = \frac{n!}{k!(n-k)!}, where nn is the total number of cards and kk is the number of cards in a hand. In this case, n=52n = 52 (total cards in a deck) and k=5k = 5 (cards in a poker hand).\newlineCalculation: C(52,5)=52!5!(52−5)!=52!5!47!C(52, 5) = \frac{52!}{5!(52-5)!} = \frac{52!}{5!47!}
  2. Total Poker Hands Calculation: Now we perform the actual calculation for C(52,5)C(52, 5).
    Calculation: C(52,5)=52!5!47!=52×51×50×49×485×4×3×2×1=2,598,960C(52, 5) = \frac{52!}{5!47!} = \frac{52 \times 51 \times 50 \times 49 \times 48}{5 \times 4 \times 3 \times 2 \times 1} = 2,598,960
  3. Calculate Heart Flushes: To find the number of possible heart flushes, we consider that a heart flush consists of all 55 cards being hearts. There are 1313 hearts in a deck, so we use the combination formula again with n=13n = 13 (total hearts in a deck) and k=5k = 5 (cards in a heart flush).\newlineCalculation: C(13,5)=13!(5!(13−5)!)=13!(5!8!)C(13, 5) = \frac{13!}{(5!(13-5)!)} = \frac{13!}{(5!8!)}
  4. Heart Flushes Calculation: Now we perform the actual calculation for C(13,5)C(13, 5).\newlineCalculation: C(13,5)=13!5!8!=13×12×11×10×95×4×3×2×1=1,287C(13, 5) = \frac{13!}{5!8!} = \frac{13 \times 12 \times 11 \times 10 \times 9}{5 \times 4 \times 3 \times 2 \times 1} = 1,287
  5. Calculate Probability of Heart Flush: To find the probability of being dealt a heart flush, we divide the number of heart flushes by the total number of poker hands.\newlineCalculation: Probability = Number of heart flushesTotal number of poker hands=1,2872,598,960\frac{\text{Number of heart flushes}}{\text{Total number of poker hands}} = \frac{1,287}{2,598,960}
  6. Probability Calculation: Now we perform the actual calculation for the probability.\newlineCalculation: Probability = 1,2872,598,960≈0.000495\frac{1,287}{2,598,960} \approx 0.000495

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