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Which of the following would you use to find the number of different combinations of six-person nominating committees that could be chosen from a class of 25 students?

Which of the following would you use to find the number of different combinations of sixperson nominating committees that could be chosen from a class of 25 stu class=

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To answer this question, we need to remember that in a committee is not important the order of the members. In this case, we can use combinations.

Combinations of k elements from n can be represented by the next formula:

[tex]nC_k=\frac{n!}{(n-k)!k!}[/tex]

Therefore, if we have that k = 6, and n = 25. Then, we have:

[tex]25C_6=\frac{25!}{(25-6)!6!}[/tex]

And since:

[tex]25C_6=\frac{25!}{(25-6)!6!}=\frac{25!}{6!(25-6)!}[/tex]

In summary, therefore, the correct option is C.

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