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A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associate. In how many different ways can this be done if the committee should have 2 trainees and 3 research associates?
Answer & Solution
Correct Answer:
Option
C
Required number of ways
$$\eqalign{ & = \left( {{}^3{C_2} \times {}^6{C_3}} \right) \cr & = \left( {{}^3{C_1} \times {}^6{C_3}} \right) \cr & = \left( {3 \times \frac{{6 \times 5 \times 4}}{{3 \times 2 \times 1}}} \right) \cr & = 60 \cr} $$
$$\eqalign{ & = \left( {{}^3{C_2} \times {}^6{C_3}} \right) \cr & = \left( {{}^3{C_1} \times {}^6{C_3}} \right) \cr & = \left( {3 \times \frac{{6 \times 5 \times 4}}{{3 \times 2 \times 1}}} \right) \cr & = 60 \cr} $$
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