Simple Combinations

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We've all been there: four designer watches, three sets of diamond cufflinks, and seven luxury cars. Which to wear? Which to drive? It's great to have all this stuff, but you can only use one of each at a time, and choosing can be hard! How many possible combinations are there, anyway?

Of course this is a ridiculous example (unless you actually do own all that stuff, in which case, congratulations), but on the GED Math test you may see problems like this. They're called counting problems, and they can look confusing. Don't worry, however: once you know the right approach, solving counting problems is as easy as, well, 1, 2, 3!

Simple counting problems have two parts: the number of variables (things that can be different), and the number of different options within each variable. If Dave has two shirts and three pairs of pants, there are two variables (shirts and pants); the first variable has two options and the second has three options.

How many different outfits could Dave make? To start with, he has two shirts. With each of these shirts, he can wear three different pairs of pants. So, the number of possible outfits can be calculated 3 × 2 = 6. Dave has six possible outfits.

To solve simple counting problems like these, always multiply the numbers of choices for each variable. If Dave has two shirts, three pants, and four hats, then the number of combinations is 2 × 3 × 4 = 24. It's that simple!

Here is a set of basic counting problems. They all include the type of calculation we looked at in this lesson; some of them include a little extra. Good luck!