A restaurant employs 16 waiters and waitresses. In how many ways can a group of 9 waiters and waitresses be chosen for the lunch shift?

Question

A restaurant employs 16 waiters and waitresses. In how many ways can a group of 9 waiters and waitresses be chosen for the lunch shift?

? ways

(The answer is NOT 320320, 43680, or 665280)

Answer 1

In a permutation, order matters. In a combination, order doesn't matter. So in this case, all the waiter/waitress positions would be all the same, this would be a combination of 16, choose 9.

I did this on the TI calculator:

₁₆C₉ = 11440