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A club consisting of 6 juniors and 8 seniors is to be formed from a group of 13 juniors and 16 seniors. How many different clubs can be formed from the group?

User Sara
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1 Answer

1 vote

Answer:

22,084,920 different clubs can be formed from the group

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:


C_(n,x) is the number of different combinations of x objects from a set of n elements, given by the following formula.


C_(n,x) = (n!)/(x!(n-x)!)

In this question:

6 juniors, from a set of 13.

8 seniors, from a set of 16.

So


T = C_(13,6)*C_(16,8) = (13!)/(6!(13-6)!)*(16!)/(8!(16-8)!) = 22084920

22,084,920 different clubs can be formed from the group

User Sergey Gazaryan
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