How many different committees can be formed from 6 teachers and 37 students if the committee consists of 4 teachers and 4 ​students?

Question

How many different committees can be formed from 6 teachers and 37 students if the committee consists of 4 teachers and 4 ​students?

The committee of 8 members can be selected in
BLANK different ways.

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Khoii Minh 3 months 2021-08-12T07:32:58+00:00 1 Answers 1 views 0

Answers ( )

    0
    2021-08-12T07:34:31+00:00

    Answer:

    The committee of 8 members can be selected in 990,675 different ways.

    Step-by-step explanation:

    The order in which the teachers and the students are chosen is not important, which means that the combinations formula is used to solve this question.

    Combinations formula:

    C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

    C_{n,x} = \frac{n!}{x!(n-x)!}

    In this question:

    4 teachers from a set of 6.

    4 students from a set of 37.

    Then

    T = C_{6,4}C_{37,4} = \frac{6!}{4!2!} \times \frac{37!}{4!33!} = 990675

    The committee of 8 members can be selected in 990,675 different ways.

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