If five cards are selected at random from a standard 52 card deck, what is the probability of getting a full house.
This is what I am thinking.
$(52*\binom{4}{3}*\binom{4}{2})/_{52}C_5$
Is that right?
Probability – How to Calculate the Probability of Getting a Full House
probability
Best Answer
A full house has three cards of one kind and two of another, so think about it like this: first you choose a type of card (13 choices), then you choose three out of four of those cards, then you choose a second type of card, and finally you choose two of those four cards. Thus you have ${13\choose 1}{4\choose 3}{12\choose 1}{4\choose 2}$ possible full house hands. So the probability is then
$${{{13\choose 1}{4\choose 3}{12\choose 1}{4\choose 2}}\over{52\choose 5}}={{(13)(4)(12)(6)}\over2598960}={3744\over2598960}\approx0.00144$$