Question

How many ways are there to pack nine identical DVDs into three indistinguishable boxes so that each box contains at least two DVDs?

Short answer

There are three methods to distribute nine indistinguishable objects into three indistinguishable boxes

Step-by-step solution

Concept Introduction

Counting is the act of determining the quantity or total number of objects in a set or a group in mathematics. To put it another way, to count is to say numbers in sequence while giving a value to an item in a group on a one-to-one basis. Objects are counted using counting numbers.

How many ways are there to pack nine identical DVDs into three indistinguishable boxes

We're trying to figure out how many different methods there are to distribute 9 indistinguishable things (identical DVDs) into three indistinguishable boxes.

We won't be able to solve this problem using a formula, therefore we'll have to figure out every conceivable combination of the number of objects in the boxes.

At least two things must be present in each of the three boxes.

\({\rm{5,2,2}}\)(5 objects in one box, 2 objects in each of the remaining boxes)

\({\rm{4,3,2}}\)(4 items in one box, 3 in another, and 2 in the third)

\({\rm{3,3,3}}\)(3 things in each of the three boxes)

Then we see that there are three methods to distribute nine indistinguishable objects into three indistinguishable boxes, each containing at least two elements.