1. The problem statement, all variables and given/known data How many four digit numbers exist where the a) the digits are strictily increasing (i.e. 1234 and 1579 but not 1338 or 1748) in size, b) decreasing in size? 2. Relevant equations 3. The attempt at a solution My problem is that I don't really have a good motivation for all this. The reasoning is something like "there are four places and nine numbers, which makes it the binominal coefficient nine over four", but it's a bit.. holey. And the guy that checks this is really strict. Anyway, that's the problem for the other one as well. I know it's the binomial coefficient 10 over 4, but how to motivate it? Tips, anyone?