Question

After a bride has interviewed 7 DJs to play at her wedding, her fiance tells her she needs to narrow it down to 4 DJs. In how many ways can she rank the 4 DJs

Answer 1

Answer:

840

Step-by-step explanation:

Given

$DJs = 7$

$To\ pick = 4$

Required

Determine the number of rankings

The term "ranking" as used in this question implies permutation and the required is calculated using:

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

Where

$n = 7$

$r = 4$

So:

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

$^7P_4 = \frac{7!}{(7-4)!}$

$^7P_4 = \frac{7!}{3!}$

$^7P_4 = \frac{7 * 6 * 5 * 4 * 3!}{3!}$

$^7P_4 = 7 * 6 * 5 * 4$

$^7P_4 = 840$

Hence, number of ranking is 840