There are 13 hearts in the deck of 52. If we want to simply choose 7 of them, we use combinatorics, and not permutations.
Thus, the total number of ways to choose 7 of the 13 hearts, is: ¹³C₇ or 1716 ways. The total in our sample space is simply choosing 7 of the 52 cards, which is: ⁵²C₇ or 133 784 560.