I have 4 assignments to pass to three different people to do for me. What is the probability that each person will receive at least one assignment?

Total combination: $\displaystyle {4+3-1\choose 3-1}$ = $\displaystyle {6\choose 2}$ = 15

P(each person receive at least one assignment) = $\displaystyle 3\over 15$ = $\displaystyle 1\over 5$

My answer is 0.2

but it's wrong

It's a MCQ question with options: (A) $\displaystyle 8\over 9$, (B) $\displaystyle 64\over 81$, (C) $\displaystyle 4\over 9$, (D) $\displaystyle 16\over 81$, (E) $\displaystyle 5\over 9$