How many ways are there to arrange $m$ distinct flags on a row of $r$ flagpoles? The order of the flags on the flagpoles (from top to bottom) matters.
My argument is: I have $mr$ points and I have to decide where to put the $m$ flags, so the result should be $\binom{mr}{m}$. But the second point of the exercise let me think that the right answer might be $m(m+1)\cdots(m+r-1)$ or $r(r+1)\cdots(r+m-1)$.
Is my argument wrong? And if it is, where is the mistake?