In how many way can a committee of 4 women and 5 men be chosen from 9 women and 7 men, if Mr. A refuse to serve on the committee if Ms. B is a member? -Maths 9th

In how many way can a committee of 4 women and 5 men be chosen from 9 women and 7 men, if Mr. A refuse to serve on the committee if Ms. B is a member? -Maths 9th
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1 Answer

Answer :

 First of all number of ways. Committees can be founded =6C3​×5C2​Now, we remove committees with both A and B =4×5C2​again we need to remove committees with B and not C =5C2​×4. Now we shall add the committees with A, not C as it has been subtracted twice =4×4C2​No. of ways =6C3​×5C2​−4×5C2​−5C2​×4+4×4C2​                     =124. Hence, the answer is =124.
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