Question

What is the probability of getting a “FULL HOUSE” in five cards drawn in a poker game from a standard pack of 52-cards?
[A FULL HOUSE consists of 3 cards of the same kind (eg, 3 Kings) and 2 cards of another kind (eg, 2 Aces)]

Options

• `6/4165`

• `4/4165`

• `3/4165`

• None of these

Answer 1

`bb(6/4165)`

Explanation:

There are 6 ways to select 2 cards of the same kind from the 4 cards in the deck and there are 13 different kinds of cards, so the total number of combinations possible of 2 cards is 6 × 13 = 78.

There are 4 ways to choose 3 cards of the same kind from 4 cards of the same kind, but because the 3-of-a-kind suit must be different from the 2-of-a-kind suit, the possible combinations of this is, 4 × 12 = 48.

So total number of ways is = 48 × 78 = 3744

Sample space is ⁵²C₅ = 2,598,560

Required Probability = `3744/2598560 = 6/4165`