Question

1. A high school is planning to put on the musical West Side Story. There are 20 singers auditioning for the musical. The director is looking for two singers who could sing a good duet.

In how many ways can the director choose two singers from the 20 singers?
Indicate if this question involves a permutation or a combination. Give a reason for your answer.

Answer 1

Answer: The director can choose two singers from the 20 singers in 190 different ways.

Explanation:

Given : The total number pf singers auditioning for the musical= 20

The number of singers looking director for = 2

We use combinations here because order of selecting singers does not matter.

(If order matters then we use permutations.)

The number of combinations of to select r things of n things =
`^nC_r=(n!)/(r!(n-r)!)`

So the number of ways can the director choose two singers from the 20 singers=
`^(20)C_2=(20!)/(2!(20-2)!)`

`=(20*19*18!)/(2*18!)=190`

Therefore , the director can choose two singers from the 20 singers in 190 different ways.