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timurjin [86]
3 years ago
9

find the probability of being delt 5 clubs and 3 cards with one of each remaining suit in 8 card poker

Mathematics
1 answer:
kumpel [21]3 years ago
5 0

Answer: 0.003757(approx).

Step-by-step explanation:

Total number of combinations of selecting r things out of n things is given by:-

^nC_r=\dfrac{n!}{r!(n-r)!}

Total cards in a deck = 52

Total number of ways of choosing 8 cards out of 52 = ^{52}C_8

Total number of ways to choose 5 clubs and 3 cards with one of each remaining suit = ^{13}C_5\times^{13}C_1\times^{13}C_1\times^{13}C_1  [since 1 suit has 13 cards]

The required probability = =\dfrac{^{13}C_5\times^{13}C_1\times^{13}C_1\times^{13}C_1}{^{52}C_8}

=\dfrac{\dfrac{13!}{5!8!}\times13\times13\times13}{\dfrac{52!}{8!44!}}\\\\=\dfrac{24167}{6431950}\\\\\approx0.003757

Hence, the required probability is 0.003757 (approx).

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