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. Answers:
A) 223
B) 776
C) 287
D) 196
E) 211
196ivision 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= 
<gadget id="calculator">70 + 105 + 21</gadget>
<output>196</output>
196   Answer:196
<result>D</result>
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.