SOLUTION: In how many ways can a committee of 5 be formed from 5 juniors and 7 seniors if the committee must have 3 seniors? Please help me. Please explain. Thanks.

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Question 1064616: In how many ways can a committee of 5 be formed from 5 juniors and 7 seniors if the committee must have 3 seniors?
Please help me. Please explain. Thanks.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
In how many ways can a committee of 5 be formed from 5 juniors and 7 seniors if the committee must have 3 seniors?

Case 1:  The committee consists of 3 seniors and 2 juniors.
Case 2:  The committee consists of 4 seniors and 1 junior.
Case 3:  The committee consists of 5 seniors and 0 juniors.


7C3∙5C2 + 7C4∙5C1 + 7C5∙5C0 = 35∙10 + 35∙5 + 21∙1 = 350 + 175 + 21 = 546 ways

Edwin