Question

How many different committees are possible from 10 professors and 24 students If each committee is made up of 2 prolessors and 10 students?

Answer 1

88,256,520

Explanation:

You want the number of 12-person committees made up of 2 professors from a pool of 10 and 10 students from a pool of 24.

Professors

The number of possible pairs of professors is ...

10C2 = 45

This is the number of ways that 2 can be chosen from 10.

Students

The number of possible groups of students is ...

24C10 = 1,961,256

This is the number of ways 10 can be chosen from 24.

Committees

For each choice of professors, any of the choices of students can finish the committee. The number of possible committees is the product of these numbers:

45 × 1961256 = 88256520

88,256,520 different committees are possible.

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Additional comment

The notation nCk is equivalent to n!/(k!(n-k)!).

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