Question

Ravi is putting 11 colored light bulbs into a string of lights. there are 3 blue light bulbs, 4 white light bulbs, and 4 orange 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

The number of distinct orders of arranging the 11 light bulbs is 46,200, found by dividing 11! by the product of the factorials of the counts of identical objects (3! * 4! * 4!).

Step-by-step explanation:

The student is asking about the number of distinct orders for arranging 11 colored light bulbs with certain colors considered identical. This is a combinatorics problem that can be solved using the formula for permutations of a multiset. Specifically, the question involves arranging 3 blue light bulbs, 4 white light bulbs, and 4 orange light bulbs.

To find the distinct orders, we use the formula for permutations of a multiset: n! divided by the product of the factorial of the counts of identical objects. In this case, the formula becomes:

Number of distinct orders = 11! / (3! * 4! * 4!)

Calculating this gives us the answer:

Number of distinct orders = 39916800 / (6 * 24 * 24)

Number of distinct orders = 46200