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A committee of 5 members is going to be formed from 3 trainees, 4 professors and 6 research associates. How many ways can they be selected, if in a committee, there are 2 trainees and 3 research associates?

A) 15
B) 45
C) 60
D) 9

Correct Answer:



C) 60

Description for Correct answer:
Required number = \( 3C_2 \times 6C_3 \)

= \( \large\frac{3!}{2!(3 - 2)!} \times \frac{6!}{3!(6 - 3)!} \)

=\( \large\frac{3 X 2 X 1}{2 X 1 X 1} \times \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 X 2 X 1 X 3 X 2 X 1} = 60\)

Part of solved Permutation and combination questions and answers : >> Aptitude >> Permutation and combination

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