The 52 cards in a shuffled deck are dealt equally among four

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?

Please include a full explination along with the correct answers, thanks!

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