Find the probability of being dealt a hand containing 5 spade, 10 hearts, 9 diamonds, and 6 clubs. Assume that a normal deck of 52 cards is used. Round your answer to four decimal places.
A)0.0333
B)0.5000
C)0.2885
D)0.0017
E)0.7692

Question

Find the probability of being dealt a hand containing 5 spade, 10 hearts, 9 diamonds, and 6 clubs. Assume that a normal deck of 52 cards is used. Round your answer to four decimal places. ​
A)0.0333
B)0.5000
C)0.2885
D)0.0017
E)0.7692

Quizplus · Accepted Answer

The total number of possible hands that can be dealt from a deck of 52 cards is
52C26 = (52!)/(26!26!) = 495,918,532,948,104.

The number of hands that contain 5 spades, 10 hearts, 9 diamonds, and 6 clubs is the product of the number of ways to choose 5 spades, 10 hearts, 9 diamonds, and 6 clubs from their respective suits, which is:

(13C5)(13C10)(13C9)(13C6) = (1,287,084)(196,125)(86,365)(13,275) = 582,353,255,604,953,125.

Therefore, the probability of being dealt a hand containing 5 spades, 10 hearts, 9 diamonds, and 6 clubs is:

582,353,255,604,953,125 / 495,918,532,948,104 ≈ 0.0017

Therefore, the best choice is D.

Find the Probability of Being Dealt a Hand Containing 5