The 52 cards in a shuffled deck are dealt equally among four players, call them a, b, c, and d. if a and b have exactly 7 spades, what is the probability that c has exactly 4 spades?

solution:

A and B have 26 cards which are 7 spades and 19 non spades.

C and D have 6 spades and 20 non spades.

13 cards are chosen randomly from 26 cards (6 spades and 20 non spades)

probability of choosing exactly 4 spades is given by

(6 / 26) × (5/ 25) × (4/24) × (3 / 23) = 3/2990