Question

A textbook search committee is considering 13 books for possible adoption. The committee has decided to select 8 of the 13 for further consideration. In how many ways can it do​ so?

Answer 1

This is asking for the number of combinations in which you can pick 8 books out of a group of 13.
The general formula for finding combinations is:
$\left(\begin{array}{ccc}n\\k\end{array}\right) = \frac{n!}{k! (n-k)!}$
For this example where n = 13, k = 8
$\frac{13!}{8! *5!} = \frac{13*12*11*10*9}{5*4*3*2*1} = 13*11*9 = 1287$