Question
A man has 15 friends out of which 7 are his relatives.
In how many ways can he invite his 9 friends in which at least 5 must be his relatives?Solution
relatives =7, not relatives = 15-7=8 You must invite 9 friends, out of which at least 5 must be relatives. You can invite in the following way: 5 out of 7 are related and 4 out of 8 are not related or 6 out of 7 are related and 3 out of 8 are not related or 7 out of 7 are related and 2 out of 8 are not related. =7C5Ă— 8C4 +(7C6Ă—8C3) +(7C7Ă—8C2) =1470+392+28=1890.
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