Question

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?

Answer 1

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.