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.

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

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

$^{12}P_{2}{=\dfrac{12!}{(12-2)!}$

$=\dfrac{12\times11\times10!}{10!}=132$

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