(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let k and n be positive integers. In how many ways are there integers a_{1}≤ a_{2}≤ ... ≤ a_{k}≤ n.

2. Relevant equations

3. 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 a_{1}, there are n integers to choose from. For the next number, there are 1 + (n-a_{1}) integers to choose from. I'm reasonable sure that I can generalise this to say that for a_{k}, there are 1+(n-a_{k-1}) integers to choose from. From that point, I'm afraid I'm lost as to where to go with this.

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# Homework Help: Inequality proof: how many ways are there a1 =< =< ak =< n?

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