$^{n}P_r$, the number of permutations of $n$ distinct objects taken $r$ at a time, equals:

$^{n}P_r = \dfrac{n!}{(n-r)!} = n(n-1)(n-2)\ldots(n-r+1)$, which is $r$ consecutive descending factors starting from $n$. Derivation: choose 1 of $n$ for the first slot, then 1 of $(n-1)$ for the second, and so on through $r$ slots. The product is the descending factorial. Option C is $^{n}C_r$ (combinations, where order doesn't matter). The difference between $P$ and $C$ is the $r!$ in the denominator, which divides out arrangement-order redundancy.