What's the answer?

Question

Michael is putting 11 colored light bulbs into a string of lights. There are 3 pink light bulbs, 4 orange light bulbs, and 4 green light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?

Answer 1

This is the multinomial problem and the answer is 11!/(3!4!4!) It's the same process as finding the anagrams of mississippi which leads to 11!/(4!4!2!). This is the total number of permutations divided by the permutations of the indistinctive components.