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Suppose that the members of a student governance committee will be selected from the 40 members of the student senate. There are 18 sophomores, 12 juniors and 10 seniors who are members of the student senate. In how many ways can the governance committee be selected, if it must be made up of 2 sophomores, 2 juniors and 3 seniors? Assume that each of the sophomores, each of the juniors and each of the seniors is equally likely to be selected for the committee.

Respuesta :

Using the combination formula, it is found that the committee can be selected in 1,211,760 ways.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem:

  • 2 sophomores from a set of 18.
  • 2 juniors from a set of 12.
  • 3 seniors from a set of 10.

They are independent, so we can just multiply them, thus:

[tex]T = C_{18,2} \times C_{12,2} \times C_{10,3} = \frac{18!}{2!16!} \times \frac{12!}{2!10!} \times \frac{10!}{3!7!} = 1211760[/tex]

The committee can be selected in 1,211,760 ways.

A similar problem is given at https://brainly.com/question/24650047

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