Question

In how many ways can four different balls be distributed among $3$ different boxes when any box can have any number of balls?

• A. $2^3-1$
• B. $4^3$
• C. $3^2-1$
• D. $3^2$

Answer 1

Answer: (B)

$4^3$

$4$ diffrent balls

$3$ boxes

Each boxes can have upto any number of balls

Each boxes can be filled in $4$ ways

There are $4$ balls

$\Rightarrow$ There are three boxes

$\Rightarrow$ Total number of ways

$=4\times 4\times 4=64ways$

Answer : $(4{)}^3$