The standard 52 card deck has 13 spades and 13 heart in total.

Since the order of the cars is not important we are dealing with combination:

C(13, 3)*C(13, 4) = 13!/(3!(13 - 3)!) * 13!/(4!(13 - 4)!) = (11*12*13/6)*(10*11*12*13/24) = 204490

There 204490 7-card hands that have 3 spades and 4 hearts.