Given a standard 52 card deck, how many ways are there to draw a 5-card hand with 2 pairs and one distinct?
Given a standard 52 card deck, how many ways are there to draw a 5-card hand with 2 pairs and one distinct?
There are 13 different ranks in a deck of cards (Ace through King). We must choose two different ranks for the pairs. This can be done in C(13, 2) ways.
Once we have chosen the ranks for the pairs, we must choose two suits for each of the ranks. Since there are 4 suits to choose from for each rank, this can be done in C(4, 2) ways for the first rank and C(4, 2) ways for the second rank.
We have 11 ranks left to choose from for the distinct card (since two are already chosen for the pairs). Once we have chosen a rank, we have 4 suits to choose from. So, there are 11 × 4 = 44 choices for the distinct card.
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