The number of ways in which n distinct balls can be put into three boxes, is

Options

A. `3n`
B. `n^(3)`
C. `3^(n)`
D. `n+3`

Answer

C

Explanation

Here, the job of putting n different balls in three boxes is divided into n sub-jods as given below:
`J_(1)` : Putting first ball in one of the three boxes.
`J_(2)`: Putting second ball in one of the three boxes.
: : : :
`J_(n)`: Putting `n^(th)` ball in one of the three boxes.
We observe that each sub-job can be completed in three ways.
So, by the fundamental principle of counting the total number of ways of putting n balls in three different boxes is
`3xx3xx3xx.......xx3=3^(n)`