Question

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:

• A. 40
• B. 41
• C. 16
• D. 32

Answer 1

Answer: (B)

Required number of ways
${=}^2{C}_1{\times }^2{C}_1{\times }^4{C}_2{+}^2{C}_1{\times }^2{C}_2{\times }^4{C}_1{+}^2{C}_2{\times }^2{C}_1{\times }^4{C}_1{+}^2{C}_2{\times }^2{C}_2{\times }^4{C}_0$
$=2\times 2\times \frac{4\times 3}{2}$
$+2\times 1\times 4+1\times 2\times 4+1\times 1\times 1$
$=24+8+8+1=41$