Question

Eight people audition for a choir. The choir director must choose one soprano, one alto, and one tenor. In how many ways can the director fill these positions A. 56 B. 336 C. 6720 D. 40,320

Answer 1

Its A

This is the number of combinations of 3 from 8

= (*8*7*6) / (3*2*1)

= 56

Answer 2

Answer: B. 336

Explanation:

Given : Eight people audition for a choir.

The choir director must choose one soprano, one alto, and one tenor.

i.e. 3 positions have to be chosen.

In this situation , we use permutations ( where order matters ).

The number of permutations of r things taken from n things is given by :-

`^nP_r=(n!)/((n-r)!)`

Similarly , the number of ways to choose 3 persons from 8 persons by director fill three positions =

`^8P_3=(8!)/((8-3)!)\\\\=(8*7*6*5!)/(5!)\\\\=8*7*6=336`

Hence, the number of ways can the director fill these positions = 336

Thus , the correct answer is B. 336 .