Question

Five students, Stella, Victoria, Alexander, Eva, and Hunter, line up one behind theother. How many different ways can they stand in line?

Answer 1

Permutations formula

$_nP_r=\frac{n!}{(n-r)!}$

where n things are chosen r at a time.

In this case, we need to find the number of permutations of n = 5 students chosen r = 5 at a time. That is,

$\begin{gathered} _5P_5=\frac{5!}{(5-5)!} \\ _5P_5=\frac{5!}{0!} \\ _5P_5=\frac{5\cdot4\cdot3\cdot2\cdot1}{1} \\ _5P_5=120 \end{gathered}$

They can stand in line in 120 different ways