Answer: there are 84 ways to find 6 students from 9 students .
Step-by-step explanation:
Since we have given that
Total number of students to a summer dance program =9
Total number of students who can be send by dance instructor = 6
Number of ways to choose 6 students from 9 students i.e.
[tex]^9C_6[/tex]
As we know the "Combination formula " i.e.
[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]
where n denotes the total number of students
r denotes the selected students
So,
[tex]^9C_r=\frac{9!}{(9-6)!6!}\\\\^9C_r=\frac{9!}{3!\times 6!}\\\\^9C_r=\frac{9\times 8\times 7}{3\times 2\times 1}\\\\^9C_r=3\times 4\times 7\\\\^9C_r=84[/tex]
Hence, there are 84 ways to find 6 students from 9 students .
