Question

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 balls is

Answer 1

$\begin{array}{c}Eachpersongetsnon-zeroballs,thereare2distributionspossible:3+1+1OR2+2+1\\ Numberofways=(\frac{3}{1})\times (\frac{5}{3})\times 2!=60\\ Numberofways=(\frac{3}{1})\times (\frac{5}{1})\times (\frac{4}{2})=90\\ So,thetotalnumberofways=60+90=150.\end{array}$