Question

In how many ways can 5 singers be selected from 8 who came to an audition?

Answer 1

Answer: There are 56 ways to choose 5 singers from 8 singers.

Explanation:

Since we have given that

Number of total singers = 8

Number of singers to be selected = 5

So, we will use "Combination":

So, number of ways to choose 5 singers from 8 singers is given by

`^8C_5\\\\=(8* 7* 6)/(3* 2* 1)\\\\=56`

Hence, there are 56 ways to choose 5 singers from 8 singers.

Answer 2

8 “choose” 5 = (8! / 5! x (8 - 5) ! )

8 “choose” 5 = (8! / 3! x 5!)

= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) /
(5 x 4 x 3 x 2 x 1) /
(3 x 2 x 1)
= (8 x 7 x 6) /
(3 x 2 x 1)
= ( 7 x 4 x 2) = 56

Therefore there are 56 ways 5 singers can be selected from 8 that came to an audition.