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What Is the Multiplication Principle of Counting?

The multiplication principle is a useful tool when counting the number of ways something can be done. The principle says something about the number of ways to order things when there are several events put together.

The principle applies to

It is easier to understand this when looking at some examples:

Example 1

Nick’s wardrobe is made up of four different t-shirts and three different pants. How many separate outfits can Nick make?

The multiplication principle says that you can find the number of ways Nick can choose one pair of pants and one t-shirt by multiplying the number of options of choosing a pair of pants with the number of options to choose a t-shirt.

Since Nick has three possibilities to choose a pair of pants and four possibilities to choose a t-shirt, Nick can make 3 4 = 12 different outfits.

Example 2

Gordon Ramsay is making a three course dinner consisting of an appetizer, a main course, and a dessert.

  • For the appetizer, he can either serve onion soup, salad or shrimp cocktail.

  • For the main course, he can serve pasta carbonara or falafel.

  • For dessert, he can serve chocolate pudding, panna cotta, fried banana, apple tart or ice cream.

How many different menus can he make?

Here, the multiplication principle says that you can find the number of menus by multiplying the number of appetizers, main courses, and desserts. Therefore, the number of menus Gordon Ramsay can make is 3 2 5 = 30.

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