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Doss [256]
3 years ago
14

8 freshmen, 9 sophomores, 9 juniors, and 7 seniors are eligible to be on a committee.

Mathematics
1 answer:
loris [4]3 years ago
6 0

Answer: 11113200

Step-by-step explanation:

We know that , the number of combination of choosing r things from n things is given by :-

^nC_r=\dfrac{n!}{r!(n-r)!}

Then , the number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors :-

Then , the number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors :-

Then , the number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors :-

^8C_4\times ^9C_5\times^9C_2\times^7C_3

=\dfrac{8!}{(8-4)!4!}\times\dfrac{9!}{(9-5)!5!}\times\dfrac{9!}{(9-2)!2!}\times\dfrac{7!}{3!(7-3)!}\\\\ =\dfrac{8\times7\times6\times5\times4!}{4!4!}\times\dfrac{9\times8\times7\times6\times5!}{4!5!}\times\dfrac{9\times8\times7!}{7!2!}\times\dfrac{7\times6\times5\times4!}{3!4!}\\\\=11113200

∴ The number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors = 11113200

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