A person has 12 friends out of which 7 are relatives. In how many ways can he invite 6 friends such that at least 4 of them are relatives?

No. of non-relative friends = 12-7=5 He may invite 6 friends in following ways: (a). 4 relatives + 2 non-relatives = ^{7C }4X^{5C}2 (b). 5 relatives + 1 non-relative = ^{7C }5X^{5C}1 (c). 6 relatives + 0 non-relative = ^{7C }6 ∴ Reqd. no. of ways = ( ^{7C }4X ^{5C}2^{)} ^{+ ( }^{ } ^{7C }5X^{5C}1^{)+ } ^{7C }6 =`(35xx10) + (21xx5) + 7 = 462`

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