Question

The total number of ways in which $5$ balls of different colour can be distributed among $3$ person so that each person gets at least one ball is

• A. $150$
• B. $3$
• C. $36$
• D. $4$

Answer 1

The correct option is A $150$

Everyone must get at least one

There one two cases satisfying this

case:- division $\to$ 2,2,1

No of distributing in that way =${}^5{C}_2{-}^3{C}_2$

$=30$

2,2,1 can be permuted ${}^3{C}_1=3$

No of ways = $30\times 3=90$

case :- division 1,1,3

no of distributing in that way ${}^5{C}_3{\times }^2{C}_1=20$

3,1,1 can be permuted ${}^3{C}_1=3$

No of ways $=20\times 3=60$

Total number of ways = 90+60 =150