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 Puzzle Solution With Explanation
by K Sengupta)
If we were required to deduce that exactly P cards belonged to the same suit, given that P are drawn from a pack of 52 cards, then proceeding similarly as before, the methodology would
be as follows:
We observe that the N cards of one suit can be chosen in
comb(13,Q), so that the remaining (P-Q) cards can be chosen out of the remaining (52-13) = 39 cards in comb(39,P- Q) 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 equal to 4*comb(13,Q)*comb(39,P-Q)
Now, the total number of ways to choose the 5 cards without any restriction = comb(52, P)
Consequently, the required probability is equal to:
4*comb(13,Q)*comb(39,P-Q)/ comb(52, P)
Substituting (P, Q) = (5, 3), we arrive at the probability sought in the given problem.
Edited on March 28, 2008, 4:45 am