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?
Explanation:
Out of the 5 girls, 3 girls can be invited in 5C3 ways. Nothing is mentioned about the number of boys that he has to invite. He can invite one, two, three, four or even no boys. Each boy can be invited or not. He can invite them in 24 ways. Thus, the total number of ways is 5C3 × (2)4 = 10 × 16 = 160.
Hence, option (b).
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