How many different 5-card hands with at least 3 hearts can be dealt from a standard deck of 52 cards?

To solve this problem, we need to consider two cases: when there are exactly 3 hearts and when there are 4 or 5 hearts.

1. Exactly 3 hearts: There are 13 hearts in a deck of 52 cards. The number of ways to choose 3 hearts from 13 is given by the combination formula "13 choose 3", which is C(13,3). For the remaining 2 cards, we have 39 cards left (52 total - 13 hearts = 39 non-hearts). The number of ways to choose 2 cards from these 39 is given by "39 choose 2", which is C(39,2). So, the total number of ways to get exactly 3 hearts is C(13,3) * C(39,2).

2. 4 or 5 hearts: Similarly, the number of ways to get exactly 4 hearts is C(13,4) * C(39,1), and the number of ways to get exactly 5 hearts is C(13,5).

Adding these cases together gives the total number of 5-card hands with at least 3 hearts.

So, the answer is C(13,3)*C(39,2) + C(13,4)*C(39,1) + C(13,5).

You can calculate the combinations using the formula C(n, k) = n! / [k!(n-k)!], where n! denotes the factorial of n.