A permutation is a way of selecting and arranging objects where order matters.
Key word: arranged.
A permutation counts arrangements where different orders produce different results.
Number of permutations of \(r\) objects from \(n\) distinct objects:
\[ ^nP_r=\frac{n!}{(n-r)!} \]If all objects are arranged:
\[ ^nP_n=n! \]How many ways can 3 students be arranged from 5 students?
\[ ^5P_3=\frac{5!}{(5-3)!} \] \[ =\frac{120}{2}=60 \]