A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is :

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Aicharya · Accepted Answer

Required number of ways $ \begin{aligned} & ={ }^2 \mathrm{C}_1 \times{ }^2 \mathrm{C}_1 \times{ }^2 \mathrm{C}_2+{ }^2 \mathrm{C}_1 \times{ }^2 \mathrm{C}_2 \times{ }^4 \mathrm{C}_1+{ }^2 \mathrm{C}_2 \times \\ & { }^2 \mathrm{C}_1 \times{ }^4 \mathrm{C}_1+{ }^2 \mathrm{C}_2 \times{ }^2 \mathrm{C}_2 \times{ }^4 \mathrm{C}_0 \\ & =2 \times 2 \times \frac{4 \times 3}{2} \\ & \quad \quad \quad 2 \times 1 \times 4+1 \times 2 \times 4+1 \times 1 \times 1 \end{aligned} $

A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at…

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