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A sales assistant is hanging 11 sweaters on a rack. He has 3 white sweaters,4 purple sweaters, and 4 green sweaters. In how many distinct orders can the sweaters be arranged if two sweaters of the same color are considered identical (not distinct)?

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ANSWER:

11550

STEP-BY-STEP EXPLANATION:

Given:

N° of sweaters are hanging = 11

N° of white sweaters = 3

N° of purple sweaters = 4

N° of green sweaters = 4

The numbers of way taht we can arrange the sweaters if two sweaters of the same color ara considered identical would be:

[tex]\begin{gathered} n=\frac{11!}{3!\cdot4!\cdot4!} \\ n=11550 \end{gathered}[/tex]

That is, there are 11550 different ways