Five cards are drawn from a pack of 52 cards. What is the probability that exactly three of them are of the same suit.

(In reply to

Answer by K Sengupta)

We observe that the three cards of one suit can be chosen in

comb(13,3), so that the remaining 2 cards can be chosen out of the remaining (52-13) = 39 cards in comb(39,2) ways.

Since there are a total of four suits to begin with, it follows that

the total number of ways to choose the 5 cards so that precisely

three of them belong to the same suit is 4*comb(13,3)*comb(39,2)

Now, the total number of ways to choose the 5 cards without any

restriction = comb(52, 5)

Consequently, the required probability is equal to:

4*comb(13,3)*comb(39,2)/ comb(52, 5)

= 0.32617047(approx.)