I want to solve the following:
Calculate the number of ways of selecting five distinct integers $x_1,x_2,x_3,x_4,x_5$ where $0\leq x_1 \lt x_2 \lt x_3 \lt x_4 \lt x_5 \leq 20$
I think this may be a problem of inclusion/exclusion, but it also might be a stars and bars problem.
Which type of problem is this, and how do I get it into a form that is more standard for such a problem? Thank you for any ideas.