How many ways are there to put a total of m tennis balls, each distinctly numbered, into n distinctly marked baskets with at most one ball in each basket?
From the problem statement, it's clear that $n \geq m.$
Step 1: Choose $m$ baskets from $n$ of them. The number of such choices is $ \binom n m.$
Step 2: Then you have $m$ balls and $m$ baskets. Place exactly one ball into a basket. There're $m!$ such ways.
Step 3: Find the total number of permutations: It's $ \binom n m$$m!$ This number is denoted by $P(n, m).$