The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that 

each person gets at least one ball is 

Clearly, required number of ways 

= Total number of ways in which 5 balls of different colours can be distributed among 3 persons - Number of ways in which at least one person gets no ball

$\begin{array}{l}=3^5-\left({ }^3{C}_1\times 2^5{-}^3{C}_2\times 1^5\right)\\ =243-96+3=150\end{array}$