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.

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing

step-by-step explanation: