Study the given information carefully and answer the question that follow:
A committee of five members is to be formed out of 3 trainees 4 professors and 6 research associates In how many different ways can this be done if____
The committee should have all 4 professors and 1 research associate or all 3 trainees and 2 professors ?
4 professors and 1 resarch associate can be selected in $$^4C_4*^6C_1 = 6$$ ways
Similarly 3 trainees and 2 professors would be selected in $$^3C_3*^4C_2$$ ways = 6
Total ways = 6+6 = 12
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