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.
A Committee is 5 in which 2 men teachers, 2 women teachers and 1 doctor are there.
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
Number of ways of selecting 2 men teachers, 2 women teachers and 1 doctor
= $$C^5_2 \times C^3_2 \times C^5_1$$
= $$\frac{5 \times 4}{1 \times 2} \times \frac{3 \times 2}{1 \times 2} \times \frac{5}{1}$$
= $$10 \times 3 \times 5 = 150$$
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