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Lesson 30: Solving Basic Combination Problems
Many problems involves determining the number of combinations that can be formed by choose items from two groups. These problems are easy once you know how to solve them. This lesson shows how.
Don't forget to watch the embedded video clip for this lesson at the bottom of the page. Please be sure to read the embedded video information and disclaimer.
Think about this problem: Joey has 3 different shirts, and 4 different pairs of pants. How many different combinations of outfits can he form using a shirt and a pair of pants?
To solve problems like this, you must multiply the two values involved. You should memorize this procedure, but also try to understand why it works. Each shirt can be worn with 4 different pairs of pants. The first shirt can be worn with 4 pairs of pants, and so can the second shirt, and so can the third shirt. That makes 4 + 4 + 4 possible combinations of outfits, which is the same as 4 x 3, which equals 12.
Try this problem: Mary has 2 shirts, 3 pairs of pants, and 4 hats. How many outfits can she form using a shirt, a pair of pants, and a hat? In this case, we multiply all 3 numbers like this: 2 x 3 = 6. 6 x 4 equals 24, which is the answer.
Remember, when you see combination problems that look like this, multiply the quantities of each type of item involved. This process is known as the counting principle.
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