Answer :
Answer: The director can choose first a lead singer and then a stand-in for the lead singer in 132 ways.
Step-by-step 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 = [tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Similarly , the number of ways to select 2 singers in an order from 12 singers
[tex]^{12}P_{2}{=\dfrac{12!}{(12-2)!}[/tex]
[tex]=\dfrac{12\times11\times10!}{10!}=132[/tex]
Hence, the director can choose first a lead singer and then a stand-in for the lead singer in 132 ways.