SOLUTION: In how many ways can a committee of 7 students be chosen from 9 juniors and 9 seniors if there must be 4 seniors in the committee?

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Question 1069219: In how many ways can a committee of 7 students be chosen from 9 juniors and 9 seniors if there must be 4 seniors in the committee?
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Case 1

There are exactly 4 seniors and exactly 3 juniors.

9 seniors choose 4 = 9C4 
 and (times)
9 juniors choose 4 = 9C3 

That's (9C4)(9C3)


Plus


Case 2

There are exactly 5 seniors and exactly 2 juniors.

9 seniors choose 5 = 9C5 
 and (times)
9 juniors choose 2 = 9C2 

That's (9C5)(9C2)


Plus


Case 3

There are exactly 6 seniors and exactly 1 junior.

9 seniors choose 6 = 9C6 
 and (times)
9 juniors choose 1 = 9C1 

That's (9C6)(9C1)


Plus


Case 4

They are all 7 seniors and no juniors.

9 seniors choose 7 = 9C7 
 
9C7


Final answer:

(9C4)(9C3) + (9C5)(9C2) + (9C6)(9C1) + (9C7)(9C0) 

(126)(84) + (126)(36) + (84)(9) + (36)(1)

10584 + 4536 + 756 + 36 = 15912

Edwin
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