Question

The no of ways in which 4 distinct balls can be put into 4 boxes labelled a,b,c,d so that exactly one box remains empty is

Answer 1

Answer: 162 ways

Step-by-step explanation:

One of four boxes should be empty. Hence any three boxes should be filled with one ball atleast.

To choose three boxes from four, there are 3 ways possible.

Choose 3 balls out of 4 to put one each in these 3 boxes. There are 3 ways possible for this.

To place one ball in each of these 3 boxes, there are 6 ways possible.

To place the remaining ball in one of the 3 boxes, there are 3 ways possible.

Hence the total number of ways you can put these balls is:

$3 \times 3 \times 6 \times 3 = 162$