# Probability - poker fullhouse

A game of poker is played with an ordinary deck of 52 cards, and each player is dealt a hand of 5 cards chosen at random. What is the probability that a player will be dealt a full house, given that the first two cards they get are of the same denomination?

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#### Solution Preview

Given that we get two cards of the same denomination (let's say they are Xs), there are two possibilities,

1) The triple of the full house is that number (i.e. we have a triple X) and another pair (say a pair of Y), OR

2) The pair of the full house is the two cards we just got (i.e. a pair of Y and a triple X).

Let's consider case 2) first,

There are 50 cards left, and 2 of them are X (since we got 2 Xs already). Our third card ...

#### Solution Summary

The probability of obtaining a poker fullhouse is determined.