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)

320

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160

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200

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Solution

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.

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