Question

Determine the probability that exactly 3 of these cards are Aces.

Determine the probability that all five of these cards are Spades.

Determine the probability that exactly 3 of these cards are face cards.

Determine the probability of selecting exactly 2 Aces and exactly 2 Kings

Determine the probability of selecting exactly 1 Jack

Answer 1

C(4,3)C(48,2)/C(52,5) - 3 of 4 aces, 2 of 48 non-aces 0.1736%

C(13,5)/C(52,5) - 5 of 13 spades 0.0495%

There are 4 face cards, ace, king, queen, jack, and 4 suits for each. 16 face cards, and 36 non-face cards - C(16,3)C(36,2)/C(52,5) 13.5747%

There are 44 cards that are not aces or kings - C(4,2)C(4,2)C(44,1)/C(52,5) 0.0609%

There is 1 jack and 48 non-jacks C(4,1)C(48,4)/C(52,5) = 29.9474%

0.1736%

 0.0495%

13.5747% 

0.0609%

  29.9474%