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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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The correct answer is:
41
41
Required number of ways
$$
\begin{aligned}
& ={ }^2 \mathrm{C}_1 \times{ }^2 \mathrm{C}_1 \times{ }^2 \mathrm{C}_2+{ }^2 \mathrm{C}_1 \times{ }^2 \mathrm{C}_2 \times{ }^4 \mathrm{C}_1+{ }^2 \mathrm{C}_2 \times \\
& { }^2 \mathrm{C}_1 \times{ }^4 \mathrm{C}_1+{ }^2 \mathrm{C}_2 \times{ }^2 \mathrm{C}_2 \times{ }^4 \mathrm{C}_0 \\
& =2 \times 2 \times \frac{4 \times 3}{2} \\
& \quad \quad \quad 2 \times 1 \times 4+1 \times 2 \times 4+1 \times 1 \times 1
\end{aligned}
$$
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