Calculate the number of permutations of \( n \) objects taken \( r \) at a time. Each calculation shows detailed step-by-step solutions with factorial expansions.
Permutation Formula
\[
nPr = P(n, r) = \frac{n!}{(n-r)!}
\]
Where \( n! = n \times (n-1) \times (n-2) \times \cdots \times 1 \) (factorial)
Order matters in permutations — different arrangements count separately.