Question

Roscoe has 17 bulbs to make a string of holiday lights. How many distinct arrangements can he make if he has 5 red bulbs, 6 green bulbs, 2 blue bulbs, and 4 yellow bulbs?

Answer 1

85,765,680

Explanation:

You want to know the number of distinct arrangements of 17 bulbs in a string if the complement of bulbs is ...

• 5 red
• 6 green
• 2 blue
• 4 yellow

Arrangements

There are 17! ways to arrange 17 bulbs. However, each of the colors of bulbs will have n! arrangements that are not distinct, where n is the number of bulbs of the same color.

This means the total number of arrangements will have to be divided by ...

(5!)(6!)(2!)(4!)

The number of distinct arrangements of the 17 bulbs is ...

17!/((5!)(6!)(2!)(4!)) = 85,765,680

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