Question

A committee of $5$ is to be formed from $9$ ladies and $8$ men, if the committee commands a lady majority, then the number of ways this can be done, is

• A. $2352$
• B. $1008$
• C. $3486$
• D. $3360$

Answer 1

The correct option is C $3486$

Number of ways of forming committee $=$ Three women $\times$ Two men $+$ Four women $\times$ one men $+$ five women

${=}^9{C}_3{\times }^8{C}_2{+}^9{C}_4{\times }^8{C}_1{+}^9{C}_5{\times }^8{C}_0=84\times 28+126\times 8+126\times 1=3486$

So option $C$ is correct.