Question

How many ways can three people be selected from a group of seven people if order does matter

Answer 1

210 ways

Explanation:

Given

`n = 7` --- total

`r = 3` --- selection

Required

In how many ways can be selection be done

Since orders does matter, then it is permutation.

This is calculated as:

`^nP_r = (n!)/((n-r)!)`

So, we have:

`^7P_3 = (7!)/((7-3)!)`

`^7P_3 = (7!)/(4!)`

Solve each factorial

`^7P_3 = (7*6*5*4!)/(4!)`

`^7P_3 = 7*6*5`

`^7P_3 = 210`