Question: Seven different objects must be divided among three persons. In how many ways this can be done if at least one of them gets exactly one object.
Options:
(A) 223
(B) 776
(C) 287
(D) 196
(E) 211 Random thoughts:
Division of m+n+p objects into three groups is given by (m+n+p)!m!n!p!(m+n+p)!m!n!p!
But 7 = 1 + 3 + 3 or 1 + 2 + 4 or 1 + 1 + 5
So The number of ways are (7)!1!3!3!12!(7)!1!3!3!12! + (7)!1!2!4!(7)!1!2!4! + (7)!1!1!5!12!(7)!1!1!5!12! = 70 + 105 + 21 = 196 The final answer: (D).