a 13card hand is dealt from a standard deck of cards What is

a 13-card hand is dealt from a standard deck of cards. What is the probability that the hand contains at least 3 cards of every suit?

Solution

There are 52c13 ways to choose 13 cards.

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To ensure there are at least 3 cards of each suit, we fix the first 12 cards. There are 13C3 ways to get 3 cards from each suit. Hence, there are (13C3)^4 ways to get the first 12 cards.

The 13th card can be any of the remaining 40 ways.

Thus, we can do this in (13C3)^4 * 40 ways.

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Thus,

P = (13C3)^4 * 40 / 52C13 = 0.421445213 [ANSWER]