There is a pile of 8 blocks: 4 are white, 3 are yellow, and 1 is purple. by placing the blocks side by side in a straight line, how many different color patterns could you make

I could make 280 different color patterns.

Step-by-step explanation:

Let's suppose that we want to arrange in a straight line N objects.

Let's also suppose that in this N objects there are N1 objects of a certain class (this N1 objects are equal between them), N2 objects of a certain class (this N2 objects are also equal between them), ... , Nn objects of a certain class.

Mathematically :

This is a condition to apply the following equation

The total ways to arrange them are :

Where ''!'' is the factorial number.

For example :

4! = 4 x 3 x 2 x 1

3! = 3 x 2 x 1

1! = 1

0! is defined as 1

In this exercise we only need to apply this equation to answer the question.

There are 8 blocks.

4 are white

3 are yellow

1 is purple

The first condition is satisfied. Now, we can apply the equation to find the arrangements.

There are 280 different color patterns.