User:Ryanbear

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stars and bars on differences

To find the number of ways to choose $n$ numbers between $a$ and $b$ if they are indistinguishable but can have duplicates let $a_1$ be the difference between the smallest number and $a$, $a_2$ be the difference between the 2rd and 1st smallest numbers, and similar logic to get $a_{n+1}$ is the difference between $b$ and the largest number. $a_1+a_2+...+a_{n+1}=b-a$. Then use stars and bars to get ${n+b-a \choose n}$