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 4X5C2 (b). 5 relatives + 1 non-relative = 7C 5X5C1 (c). 6 relatives + 0 non-relative = 7C 6 ∴ Reqd. no. of ways = ( 7C 4X 5C2) + ( 7C 5X5C1)+ 7C 6 =`(35xx10) + (21xx5) + 7 = 462`
