Question

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?

Answer 1

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:

`nC_k=(n!)/((n-k)!k!)`

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

`25C_6=(25!)/((25-6)!6!)`

And since:

`25C_6=(25!)/((25-6)!6!)=(25!)/(6!(25-6)!)`

In summary, therefore, the correct option is C.