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A committee of five members is to be formed out of 3 Teachers, 4 Assistants and 6 Students. In how many ways can it be done so that the committee either has all 4 Assistants and 1 Student or all 3 Teachers and 2 Assistants?

A committee of five members is to be formed out of 3 Teachers, 4 Assistants and 6 Students. In how many ways can it be done so that the committee either has all 4 Assistants and 1 Student or all 3 Teachers and 2 Assistants? Correct Answer 12

4 Assistants and 1 Student can be selected in 4C4 × 6C1 = 6 ways

3 Teachers and 2 Assistants can be selected in 3C3 × 4C2 = 6 ways

∴ Total ways = 6 + 6 = 12

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