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 included together in the committee, then the number of committees formed is

• A. $420$
• B. $540$
• C. $336$
• D. $216$

Answer 1

The correct option is C $336$

Total ways without restriction is $={}^7{C}_5\cdot {}^6{C}_3$
Total ways when the two particular ladies are included together is $={}^7{C}_5\cdot {}^4{C}_1$
$\therefore$The total number of committes formed is
${}^7{C}_5\cdot {}^6{C}_3-{}^7{C}_5\cdot {}^4{C}_1=336$