What is the probability of getting full house in five-card poker given the following cards are missing?
Missing cards: $\heartsuit$2, $\heartsuit$5, $\heartsuit$10, $\heartsuit$Jack, $\heartsuit$King
My attempt on trying to solve this was to first calculate the combinations of hands which gives full house and then remove the combinations of the missing cards. This is what I came up with:
$\displaystyle \frac{{13\choose 1}{4\choose 3}{12\choose 1}{4\choose 2}-{8\choose 5}{1\choose 1}}{{47\choose 5}}$
But I'm not sure this is a valid method... Any tips on how to approach the problem?