Question

Of 14 possible books, you plan to take 5 with you on vacation. How many different collections of 5 books can you take?

Answer 1

Since the problem does not take the order into account this is a combination problem.

A combination is given by:

$_nC_k=\frac{n!}{k!(n-k)!}$

Then in this case we have:

$_{14}C_5=\frac{14!}{5!(14-5)!}=2002$

Therefore there are 2002 different collections of five books