Let k and n be positive integers. In how many ways are there integers a1≤ a2≤ ... ≤ ak≤ n.
The Attempt at a Solution
I don't really know where to begin. Simply using permutations doesn't seem to work. I know that for a1, there are n integers to choose from. For the next number, there are 1 + (n-a1) integers to choose from. I'm reasonable sure that I can generalise this to say that for ak, there are 1+(n-ak-1) integers to choose from. From that point, I'm afraid I'm lost as to where to go with this.