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=(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=(5!)/((5-5)!) \\ _5P_5=(5!)/(0!) \\ _5P_5=(5\cdot4\cdot3\cdot2\cdot1)/(1) \\ _5P_5=120 \end{gathered}`

They can stand in line in 120 different ways