This tag is for basic questions about the study of finite or countable discrete structures — specifically how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions. ...
This is a generalization of this question. An $(n,k)$ partial permutation is an injection from $[k]$ to $[n]$. It can be thought of as word of length $k$ in symbols in $[n]$ without duplications. ...