Question: In how many ways can you sort 8 of 12 flags (4 flags for each country) so there will be at least one flag from each country? Final answer: 4620
I'm not sure whether it's possible, but I'd like to solve this question by reducing the impossible ways from the total options. I think that there are ${3 \choose 1}\dfrac{8!}{4! 4! 0! }$ impossible ways of sorting. How can the total options be calculated? I assume that the flags of the same country are indistinguishable.
Thanks!