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. 320
• B. 160
• C. 80
• D. 200

Answer 1

The correct option is B 160

Option (b) 3 girls can be selected out of 5 girls in ⁵C₃ ways. Since the number of boys to be invited is not to be given, he can invite or not invite them in 2⁴ ways.

Hence required numbers of ways =⁵C₃ × 2⁴= 10 × 16 = 160.