There are two variations I would like to discuss about this problem that I have encountered and haven't been able to solve previously.

1) Shuffling is introduced i.e when order/arrangement matters. Suppose We have infinte (or >=N) flags of each of r colors. We have to find an arrangement of N flags using these flags . How many ways can this be done. (So a1 + a2 + .... ar = N where ai is number of flags of color i but since this is an arrangement, shuffling within the N flags is possible).

2) No shuffling but similar sets should be counted only once. i.e (a1,a2,a3) = (1,1,2) is same as (a1,a2,a3) = (2,1,1)

Also, what is a good blog/site/resource for intermediate-hard counting/combinatorics problems (with editorials/theory).