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Instructions
From the following, differen committees are to be made as per the requirement given in each question.
In how many different ways can it de done? 10 men and 8 women out of which 5 men are teachers, 3 men doctors and businessmen. Among the women, 3 are 2 are teachers, 2 doctors, 2 researchers and 1 social worker.
Solution
Out of 10 men, Teachers = 5
Doctors = 3 and Business man = 2
Out of 8 women, Teachers = 3 and Doctors = 2
Researchers = 2 and Social worker = 1
Now, no teacher and doctor should be selected.
=> Remaining members (both men and women) = (2) + (2 + 1) = 5
Thus, number of ways of selecting 3 people out of 5
= $$C^5_3 = \frac{5 \times 4 \times 3}{1 \times 2 \times 3} = 10$$
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