There are 6 boys and 3 girls in a class. An entertainment committee of 5 is to be selected such that their are 3 boys and 2 girls in a committee. In how many ways can the committee be selected? What are the number of ways if their is at least one girl?

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Please find below the solution to the asked query:

We have 6 boys and 3 girls.Number of ways of selecting 3 boys=6C3Number of ways of selecting 2 girls=3C2Required number of ways=6C3×3C2=6×5×43×2×1×3×22×1=20×3=60AnswerAs there should be atleast one girl, hence committee can be as follows:4 boys AND1 girlOR3 boys AND2 girlOR2 boys AND3 girlRequired number of ways=6C4×3C1+6C3×3C2+6C2×3C3=6×5×4×34×3×2×1×31+6×5×43×2×1×3×22×1+6×52×1×3×2×13×2×1=45+60+15=120Answer

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