aaratigarlapati wrote:

In how many ways 5 different balls can be arranged in to 3 different boxes so that no box remains empty?

How can we feel three boxes with 5 balls?

3 + 1 + 1

2 + 2 + 1

With 3,1,1 distribution:

How many ways to select 3 from 5?

5!/3!2! = 10

How many ways to select 1 ball from 2?

2!/1! = 2

How many ways to select 1 ball from 1?

1!/1! = 1

How many ways to distribute 3,1 and 1 to 3 boxes? 3!/2! = 3

10*2*3 = 60

With 2,2,1 distribution:

How many ways to select 2 from 5?

5!/2!3! = 10

How many ways to select 2 from 3?

3!/2!1! = 3

How many ways to select 1 from 1?

1

How many ways to distribute 2,2,1 to 3 boxes? 3!/2! = 3

10*3*3=90

90+60 = 150

Answer: 150

_________________

Impossible is nothing to God.