A hand consists of 5 cards dealt from a standard deck of 52 cards. order of the cards doesn't matter. Determine the probabilities for a 5-card poker hand. in percent form, rounded to 4 decimal places.

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

1. C(4,3)C(48,2)/C(52,5) - 3 of 4 aces, 2 of 48 non-aces 0.1736%
2. C(13,5)/C(52,5) - 5 of 13 spades 0.0495%
3. 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%
4. There are 44 cards that are not aces or kings - C(4,2)C(4,2)C(44,1)/C(52,5) 0.0609%
5. There is 1 jack and 48 non-jacks C(4,1)C(48,4)/C(52,5) = 29.9474%

Note: Excel uses combin for combinations.