I've forgotten the methodology for deducing the number of ways to select N groups from M objects. For example, if I had 11 flags, how many ways would there be to put the 11 flags in 5 piles?
The real question I'm working on is:
"How many integer solutions are there to the equation x1 + x2 + x3 + x4 + x5 = 21, if xi >= 2 for i = 1, 2, 3, 4, 5."
I was going to try and think about it as having 5 groups of at least 2 (since each xi much be at least 2) and then distribute the remaining 11 groups of 1 between the 5 groups.