Number of distinct $n-l$ digit numbers from $n$ digits some of which are repeated?

Question

How to solve this combinatorics problem? I have $n$ digits, such that $m$ of them are equal and the other $k$ are equal ($n = m+k$). How many distinct $n-l$ digit numbers can I make? (Here $l$ is an integer such that $1 \leq l < n$). For example I have $3, 3, 3, 2, 2$ and I want to make a 4 digit number. Here $n =5$, $m = 3$, $k = 2$ and $l=1$.

Thanks!

Answer 1

I would have thought you want something like $$\sum\limits_{j=\max(0,m-l)}^{\min(m,n-l)} {n-l \choose j}$$ which in your example is ${4 \choose 2}+{4 \choose 3} =6+4=10$