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# At a Glance - Basic Counting Principle

Now that you have learned all the hard ways to chart possible outcomes using organized lists, tree diagrams, and area models, it's time to learn the elegant short cut.

Basic counting principle: to find the total possible outcomes for two or more events, simply multiply the possible outcomes for each event together

Total Outcomes = # of outcomes for event 1 × # of outcomes for event 2 × # of outcomes for event 3, and so on…

#### Example 1

 There are 4 different coins in this piggy bank and 6 colors on this spinner. If you pick 1 coin and spin the spinner:a) how many possible outcomes could you have?b) what is the probability that you will pick a quarter and spin a green section?

#### Example 2

 If you spin each of these spinners...a) how many different combined outcomes could you get?b) what is the probability that both spinners land on the same color?

#### Example 3

 A pizza parlor allows you to choose between thin or thick crust, whole wheat or plain dough, spicy or regular tomato sauce, and four different types of cheese all before you decide on your toppings. a) How many different pizzas can you make from these selections?b) Assuming all options are chosen equally, what is the probability that a thin crust, whole wheat pizza with spicy sauce will be ordered?

#### Exercise 1

What is the probability of flipping a coin four times in a row and having it land on heads each time?

#### Exercise 2

If you are allowed to choose one fruit, one sandwich, and one bag of chips, how many different lunches can be made from these choices: apple, orange, banana, PB&J on whole wheat, turkey and Swiss on sourdough, tuna salad on rye, Fritos, Cheetos, Nacho Cheese Doritos, or Sunchips?

#### Exercise 3

If you pick one card each from two decks of cards, what is the probability that both cards will be the Ace of Spades?