Counting FULL HOUSE Hands in Poker | Combinatorics

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Counting Poker Hands
Poker: Poker is played with a 52 card deck. Each card has two attributes, a rank and a suit. The rank of a card can be any of 13 possibilities:
{2, 3, 4, 5, 6, 7, 8, 9, 10,J,Q,K,A}, while the suit can be any of 4 possibilities:
{♣, ♦, ♥, ♠}. We exclude jokers and wildcards.

Full house: This consists of three cards of one rank and two cards of another rank. Thus, the number of full house hands is 3744.

(Poker & Probability) Probability of getting a Full House:
In a standard 52-card deck poker hand, there are 3,744 possible full houses. This is calculated by choosing the rank for the three of a kind (13 options), then selecting three suits out of four (4C3 = 4), then choosing the rank for the pair (12 options), and finally selecting two suits out of four (4C2 = 6), resulting in 13 * 4 * 12 * 6 = 3744.

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