From a deck of 52 cards, a 7 card hand is dealt.How many distinct hands are there if the hand must contain 2 spades and 3 diamonds ?

There are 13 spades,we must include 2: 13 $C2$

There are 13 diamonds,we must include 3:  $13C3$

Since we can't have more than 2 spades and 3 diamonds,the remaining 2 cards must be pulled out from the 26 remaining clubs and hearts :  $26C2$

Therefore, $13C2*13C3*26C2$ = 7250100