Hand of Poker Probability I'm not sure about how to solve the following problem
Randomly draw 5 cards from a deck of cards. What is the probability of getting two pairs and one
of the 5 cards is Heart-7 (♥7)?
I solved it this way:
Case 1 (7 is a pair): (3C1)(12C1)(4C2)(11C1)
Case 2 (7 is not a pair): (12C2)(4C2)^2
So the probability is: ((3C1)(12C1)(4C2)(11C1) +(12C2)(4C2)^2)/(52C5)
But I think I'm missing something

Not quite. In the first case there are actually $44$ possibilities for the odd card, not $11$: it can be any of the $44$ cards of denominations different from those of the two pairs. If you prefer, it’s $\binom{11}1\binom41$: $11$ ways to choose the odd denomination, and $4$ ways to choose one card of that denomination.
