Question

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

Answer 1

Answer:

210 ways

Step-by-step 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:

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

So, we have:

$^7P_3 = \frac{7!}{(7-3)!}$

$^7P_3 = \frac{7!}{4!}$

Solve each factorial

$^7P_3 = \frac{7*6*5*4!}{4!}$

$^7P_3 = 7*6*5$

$^7P_3 = 210$