Answer:
840
Step-by-step explanation:
Given
[tex]DJs = 7[/tex]
[tex]To\ pick = 4[/tex]
Required
Determine the number of rankings
The term "ranking" as used in this question implies permutation and the required is calculated using:
[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]
Where
[tex]n = 7[/tex]
[tex]r = 4[/tex]
So:
[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]
[tex]^7P_4 = \frac{7!}{(7-4)!}[/tex]
[tex]^7P_4 = \frac{7!}{3!}[/tex]
[tex]^7P_4 = \frac{7 * 6 * 5 * 4 * 3!}{3!}[/tex]
[tex]^7P_4 = 7 * 6 * 5 * 4[/tex]
[tex]^7P_4 = 840[/tex]
Hence, number of ranking is 840
The required number of ways is 840.
Important information:
We need to find a number of ways to rank 4 DJs.
It means we need to find the permutation P(7,4).
[tex]P(7,4)=\dfrac{7!}{(7-4)!}[/tex]
[tex]P(7,4)=\dfrac{7\times 6\times 5\times 4\times 3!}{3!}[/tex]
[tex]P(7,4)=7\times 6\times 5\times 4[/tex]
[tex]P(7,4)=840[/tex]
Therefore, the required number of ways is 840.
Find out more about 'Permutation' here:
https://brainly.com/question/1285879
