Question

From a group of $8$ women and $6$ men, a committee of $3$ men and $3$ women is to be formed. In how many ways can the committee be formed if two of the women refuses to serve together?

• A. $1020$
• B. $1000$
• C. $712$
• D. $896$

Answer 1

The correct option is D $896$

$2$ women refuse to serve together say women A and Women B.

There are three conditions.

1. If Women A is selected and B is not selected.

${=}^8{C}_3{\times }^4{C}_2=336$ (1)

2. If women B is selected and A is not selected.

${=}^8{C}_3{\times }^4{C}_2=336$

3. Both are not selected.

${=}^8{C}_3{\times }^4{C}_3=224$

Total Number of ways $=896$