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.