Question

The entire deck of 52 cards is dealt out to 4 players

Find the probability that one player receives 6 spades and another player receives 7 spades.

Answer 1

52 cards is dealt out to 4 players.

P(One player receive 6 spades and other player receive 7 spades)

=P(One player receive 6 spades) +P(Other player receive 7 spades)

=(6/52). (5/51) (4/50) (3/49) (2/48) (1/47) +(3*(7/46) (6/45) (5/44) (4/43) (3/42) (2/41) (1/40)

(3 is remaining players.)

=(4.91194841*10^-8) +(5.60489106*10^-8)

=10.51683947*10^-8

The probability that one player receives 6 spades and another player receives 7 spades is 10.51683947*10^-8 or (10.51683947*10^-6 %).