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.\nOptions:\n(A) 223\n(B) 776\n(C) 287\n(D) 196\n(E) 211 Stream of consciousness:
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!\nBut 7 = 1 + 3 + 3 or 1 + 2 + 4 or 1 + 1 + 5\nSo 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
Thus, the answer is (D).
Assistant