How many different signals can be made by hoisting two yellow flags, three green flags, and five red flags on a ship's mast at the same time? i tried doing (11 c 2)(11 c 3)(11 c 5) and that doesn't work.

Given:
2 yellow flags
3 green flags
5 red flags

for a total of 10 flags.

It is a permutation of 10 objects, not all distinct.

The number of permutation is: 
     10!            3,528,800
=    = 2,520
2! * 3! * 5!        1,440

There are 2,520 different signals that can be made using the given flags.