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.

Step-by-step 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 = $^nC_r=\dfrac{n!}{r!(n-r)!}$

So the number of ways can the director choose two singers from the 20 singers=$^{20}C_2=\dfrac{20!}{2!(20-2)!}$

$=\dfrac{20\times19\times18!}{2\times18!}=190$

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