Question

A committee of $5$ men and $3$ women is to be formed out of $7$ men and $6$ women. If two particular women are not to be together in the committee, the number of committees formed is

• A. $420$
• B. $5040$
• C. $336$
• D. $216$

Answer 1

Answer: (C)

$336$

Committee of 5 men and 3 women is to be formed and two particular women(say A and B) are not to be together then there will be 3 cases
case 1)
5men, A and two women from remaining 4 (exclude B)
${}^7{C}_5{\times }^4{C}_2$
case 2)

5men, B and two women from remaining 4 (exclude A)
${}^7{C}_5{\times }^4{C}_2$
case 3)
5 men, 4 women (excluding A and B both)
${}^7{C}_5{\times }^4{C}_3$
Required ways ${}^7{C}_5{\times }^4{C}_2{+}^7{C}_5{\times }^4{C}_2{+}^7{C}_5{\times }^4{C}_3=336$