SOLUTION: Out of 11 biologists and 6 physicists, a committee consisting of 8 biologists and 2 physicists is to be formed. In how many ways can this be done if two particular biologist canno

Question 1098474: Out of 11 biologists and 6 physicists, a committee consisting of 8 biologists and 2 physicists is to be formed. In how many ways can this be done if two particular biologist cannot be on the committee together?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
Out of 11 biologists and 6 physicists, a committee consisting of 8 biologists and 2 physicists is to be formed. In how many ways can this be done if two particular biologists cannot be on the committee together?

So there are 2 "restricted" biologists and 9 non-"restricted" biologists.

So the committee consists of either:

Case 1: 1 restricted biologist, 7 non-resticted biologists, and 2 physicists.  

Choose the 1 restricted biologist in 2C1 ways.  (2 choose 1)
Choose the 7 non-restricted biologists in 9C7 ways. (9 choose 7)
Choose the 2 physicists in 6C2 ways. (6 choose 2)

That's (2C1)(9C7)(6C2).

          OR

Case 2: 8 non-restricted biologists, and 2 physicists.  

Choose the 8 non-restricted biologists in 9C8 ways. (9 choose 8)
Choose the 2 physicists in 6C2 ways. (6 choose 2)

That's (9C8)(6C2).

Total for both cases:  (2C1)(9C7)(6C2) + (9C8)(6C2)

Edwin

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