How many different vertical arrangements are there of 10 flags if 5 are white, 3 are blue, and 2 are red?

Approach Because there are nondistinct items and order matters, use the formula for finding the number of permutations with nondistinct items. We seek the number of permutations of n = 10 objects, of which n₁ = 5 are of one kind (white), n₂ = 3 are of a second kind (blue), and n₃ = 2 are of a third kind (red).