Answer:
22,084,920 different clubs can be formed from the group
Step-by-step explanation:
The order in which the students are chosen to the club is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
6 juniors, from a set of 13.
8 seniors, from a set of 16.
So
[tex]T = C_{13,6}*C_{16,8} = \frac{13!}{6!(13-6)!}*\frac{16!}{8!(16-8)!} = 22084920[/tex]
22,084,920 different clubs can be formed from the group
