In how many ways can you paint 90 distinct buckets?

Question

In how many ways can you paint 90 distinct buckets, if 25 of them must be painted red, 40 of them must be painted blue, and 25 of them must be painted green?

I am right to assume that these object are mutually exclusive, if so am I right to say that the answer would be 25^90 + 40^90 + 25^90?

Answer 1

Choose 25 of the 90 buckets to be red, 25 of the remainder to be green. The remaining 40 must automatically be blue.

$\binom{90}{25}*\binom{65}{25}=\frac{90!}{65!25!}*\frac{65!}{25!40!}=\frac{90!}{(25!)^240!}$