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Counting principle

If event M has m possible outcomes and event N has n possible outcomes, then event M followed by event N has m × n possible outcomes.

Find the total number of outcomes when a coin is tossed and a number cube is rolled. There are 12 different outcomes.

The school lunch menu has the following choices. How many different lunches can be made with one choice from each column?

 Sandwich Drink Desert Hamburguer Pizza Grilled Cheese Milk Soda Ice cream Cookies Fruit

The counting principle states that if one activity can occur in m ways and another activity con occur in n ways, then both activities can occur in mn ways.

In this example, there are 3x2x3 or 18 different lunches.

A tree can show the lunch choices. 