Question

How many ways are there to distribute six indistinguishable objects into four indistinguishable boxes so that each of the boxes contains at least one object?

Short answer

There are two ways to arrange six indistinguishable objects into four indistinguishable boxes so that each of the boxes contains at least one object.

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 distribute six indistinguishable objects 

We're trying to figure out how many different methods there are to distribute six indistinguishable objects into four 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 one element must be present in each of the four boxes

(3 objects in one box, 1 in each of the three other boxes)

(2 objects in two boxes each, 1 in each of the other two boxes)

Then, we see that there are two ways to arrange six indistinguishable objects into four indistinguishable boxes, with at least one element in each box.