Seven different objects must be divided among three persons.
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.
Answer/Solution
196
Steps/Work
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
Answer:D
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
Answer:D