An art store has four brands of paint pens in 12 different colors with three types of ink. How many paint pens are there to choose from?
Let’s break down the information we were given. First of all, we know that there are four brands. We’ll call them Brand A, Brand B, Brand C, and Brand D. We know that each of these brands has 12 different colors. What we’re looking at so far is all 12 colors that each brand offers. Each brand in each color offers three different types of ink. And that means, for every single dot on this screen, we would have to break that down into three different types of ink.
Here’s an example of one color and three different types of ink from one brand. If we had to draw three different kinds of ink for all 12 colors in all four brands, we will be drawing quite a lot. So we think, there has to be a better way, right? There actually is.
When we work with combinations like this, we can use multiplication. By multiplying the number of brands by the number of colors by the types of ink, we can find how many paint pens there are to choose from. We multiply our four brands by our 12 colors. And then we multiply that by the three inks.
We can start by multiplying 12 times four which equals 48. And then we take that 48 and we multiply it by the three different types of ink, 48 times three. We start all the way on the right. And we multiply three times eight, which equals 24. We write down our four and carry our two. Then we multiply three times four, which equals 12, and add this two that we carried over, to equal 14. So we write down 14. 48 times three equals 144.
This art store sells 144 different paint pens.