142k views
2 votes
7. There are 12 singers auditioning for the school musical. In how many ways can the director choose first a lead singer and then a stand-in for the lead singer?

User Changa
by
6.7k points

1 Answer

3 votes

Answer: The director can choose first a lead singer and then a stand-in for the lead singer in 132 ways.

Explanation:

Given : The total number of singers auditioning for the school musical.= 12

The director wanted choose first a lead singer and then a stand-in for the lead singer.

We use Permutations here because order of selecting the singers matters.

The number of permutations of selecting r things out of n things =
^nP_r=(n!)/((n-r)!)

Similarly , the number of ways to select 2 singers in an order from 12 singers


^(12)P_(2){=(12!)/((12-2)!)


=(12*11*10!)/(10!)=132

Hence, the director can choose first a lead singer and then a stand-in for the lead singer in 132 ways.

User Burzumko
by
7.4k points