The Student Room Group

Probability Q.

I expect when i hear the answer i'm going to kick myself but nonetheless:

A pack of cards consists of 52 different cards. A malicious dealer changes one of the cards for a 2nd copy of another card in the pack and he then deals the cards to four players, giving thirteen to each. The probability that one player has two identical cards is?
Reply 1
P(Player 1 gets both of the identical cards)
= [50!/(11!*13!^3)] / [52!/(13!^4)]
= 1/17

P(Some player gets both of the identical cards)
= 4/17

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