How many different strings of lights can be created by placing 40 coloured lights on a horizontal string?

Question

How many different strings of lights can be created by placing 40 coloured lights on a horizontal string if 12 of them are red, 6 are blue, 14 are green and 8 are yellow? Assume that lights of the same colour are indistinguishable.

Answer 1

Hint

Think about combinations. Pick 12 positions of 40 that will be red, pick 6 out of the remaining 40-12 that will be blue, and pick 14 out of the remaining 40-12-6 that will be green. The rest will have to be yellow.

Answer 2

This is simply permutations with repeated elements, so directly use the appropriate formula to get $\dfrac{40!}{12!6!14!8!}$