# Answer to Question #26155 in Statistics and Probability for liz

Question #26155

The question is I have 52 cards with a deal of 8 cards.& I need to get probability of getting 4 face cards and 4 other cards.&

Expert's answer

The question is I have 52 cards with a deal of 8 cards. I need to get probability of getting 4 face cards and 4 other cards.

There are

N = C(52, 8) = 752538150

ways to choose 8 cards from the deck of 52 cards and there are

F = C(52-12, 4) = C(40, 4) = 91390

ways to choose 4 face cards from the same deck. Therefore, there are

M = F + C(52-4, 4) = 91390 + 194580 = 285970

ways to choose 4 face cards and 4 other cards from the deck. So, the probability of getting 4 face cards and 4 other cards is

P = M/N = 285970/752538150 ≈ 0.00038.

There are

N = C(52, 8) = 752538150

ways to choose 8 cards from the deck of 52 cards and there are

F = C(52-12, 4) = C(40, 4) = 91390

ways to choose 4 face cards from the same deck. Therefore, there are

M = F + C(52-4, 4) = 91390 + 194580 = 285970

ways to choose 4 face cards and 4 other cards from the deck. So, the probability of getting 4 face cards and 4 other cards is

P = M/N = 285970/752538150 ≈ 0.00038.

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