What is the probability of drawing a full house from a standard 52-card deck of playing cards?

Question

What is the probability of drawing a full house from a standard 52-card deck of playing cards?

Answer 1

If you're asking for the probability of drawing a full house in 5 cards, let's count the number of ways to get a full house and divide by the number of hands:

3 of a kind and 2 of a kind:

13 * (4 choose 3) * 12 * (4 choose 2) = 3744

This gives you 3 of the four cards of one value, and 2 of the four cards of a different value.

The total number of hands is simply 52 choose 5.

So that means the probability is:

P = 3744 / (52 choose 5) = 3,744 / 2,598,960 = 6 / 4165

Answer 2

Probability Full House

Answer 3

there are 26 red cards out of the 52 so it is 26/52=1/2

Answer 4

approx 1 in 694