There is a way to get an exact answer without regard for probability. Just construct the rectangular row. Say in the case of n=6, looking for two hearts, we proceed:
(An x represents a heart and a blank representing a space, and where I had to put some s's for space, since it condensed it otherwise.)
In this particular case we will have to continue for 6C2 = 15 rows within our 6 columns. So, therefore you can do 15 lines, say using Excel, and determine the total matrix for all outcomes based on an equal probability for each case. Then just add up the cases.