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:
user
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).
assistant