Question

A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them if there have to be exactly 3 girls in the invitees? (CAT 1996)

• A. 160
• B. 160
• C. 240
• D. 120

Answer 1

The correct option is B 160

Option (b) 3 girls can be selected out of 5 girls in ${}^5{C}_3$ ways. Since the number of boys to be invited is not to be given, he can invite or not invite them in $2^4$ ways.

Hence required numbers of ways ${=}^5{C}_3\times 2^4=10\times 16=160$.