In how many ways could this be done?

I think I've solved the problem, but It's an ugly solution based on brute force observation and not really comprehension.

So I realized that if you take combinations of 1 book out of 15 and sum them with combinations of 2 out of 15 ... and so on until 14 out of 15, you will probably solve this problem. I tried and got 32766 combination by doing:

(15 over 1)+(15 over 2)+(15 over 3) +...+ (15 over 14) = 32766

This feels really dirty and there should be a much more elegant way of solving this and similar kind of problems.