142,506 different five-member committees can be made.
If we have a set of N elements, the number of different subsets of K elements that we can make out of these N elements is:
[tex]C(N, K) = \frac{N!}{K!*(N - K)!}[/tex]
In this particular case, the set has 30 elements which are the students. And the committee has 5 members, so K = 5 and N = 30, then we get:
[tex]C(30, 5) = \frac{30!}{(30 - 4)!*5!} = \frac{30*29*28*27*26}{5*4*3*2*1} = 142,506[/tex]
This means that 142,506 different five-member committees can be made.
If you want to learn more about combinations:
https://brainly.com/question/11732255
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