Question

Wilson Middle Schooi is selecting students to be in the spring festival show. Theie are 5 roles left but there are 9 students interested in the roles. How many combinations of the nine students can be chosen for the five remaining roles?

Answer 1

Answer: 126

The answer to the question is 126 combinations. For n ≥ r ≥ 0.

Answer 2

126

Explanation:

It is given that in the spring festival show, there are 5 roles left but there are 9 students interested in the roles.

We need to find the combinations of the nine students can be chosen for the five remaining roles.

It means we have to find the value of
`^9C_5`.

The combination formula:

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

Substitute n=9 and r=5.

`^9C_5=(9!)/(5!(9-5)!)`

`^9C_5=(9* 8* 7* 6* 5!)/(5!4!)`

`^9C_5=(9* 8* 7* 6)/(4* 3* 2* 1)`

`^9C_5=126`

Therefore, the number of combinations is 126.