Question

Raina is putting 13 colored light bulbs into a string of lights. There are 5 white light bulbs, 6 orange light bulbs, and 2 blue 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

Answer: The number of ways would be 36,036.

Step-by-step explanation:

Since we have given that

Number of white light bulbs = 5

Number of orange light bulbs = 6

Number of blue light bulbs = 2

Total number of light bulbs = 13

So, the number of distinct orders of light bulbs if two bulbs of the same color are considered identical.

$N=\dfrac{n!}{r!}\\\\N=\dfrac{13!}{5!\times 6!\times 2!}\\\\N=36036$

Hence, the number of ways would be 36,036.