Answer:
126
Step-by-step 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 [tex]^9C_5[/tex].
The combination formula:
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Substitute n=9 and r=5.
[tex]^9C_5=\dfrac{9!}{5!(9-5)!}[/tex]
[tex]^9C_5=\dfrac{9\times 8\times 7\times 6\times 5!}{5!4!}[/tex]
[tex]^9C_5=\dfrac{9\times 8\times 7\times 6}{4\times 3\times 2\times 1}[/tex]
[tex]^9C_5=126[/tex]
Therefore, the number of combinations is 126.
