Question

Number of ways in which 5 distinct balls can be put into 3 district boxes with no restrictions is

• A. $160$
• B. $243$
• C. $150$
• D. $147$

Answer 1

The correct option is B $243$

The no: of ways of in $n$ distinct objects can be put into identical boxes , so that neither one of them remains empty.

Since both the boxes and the balls are differend , we can choose any box , and every choice is different at any time.

The first ball can be placed in any of the three boxes . Similarly , the $2^{nd},3^{rd},4^{th}$ and $5^{th}$ ball , each can be placed in any of the three boxes.

$\therefore$ No: of arrangement =$3\times 3\times 3\times 3\times 3=3^5=243$