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.)

Posted by K Sengupta on 2008-03-24 12:42:59