Question

Find the number of ways of distributing 8 similar balls into 4 different boxes so that none of the boxes are empty.

• A.
• B. 8! × 3!
• C.
• D.
• E.

Answer 1

The correct option is E

Soln:

This is a type of “similar to different” questions with a lower limit of 1.

Let the 4 boxes be A,B,C,D

A+B+C+D=8

Applying a lower limit of 1

A+B+C+D=4

Applying 0’s and 1’s method:

No. of zeroes = 4 , No. of ones = 3

Total number of ways =$\frac{7!}{(4!3!)}$. Hence option (e)