Fundamental Counting Principle

Fundamental Counting Principle

M8 Lesson 68

How many outfits does Tommy have?

• He has three different shirts: red, yellow and green.

• He has two different pairs of pants: blue and brown.

• He has a belt that he can wear or not wear.

• How many outfits does Tommy have?

How many outfits does Tommy have?

What's for lunch?

• Katie's Cafe offers three entrees for lunch: soup, salad, or soufle.

• She has three choices for the main course: roast beef, chicken or salmon.

• There are four choices for dessert: chocolate cake, strawberry trifle, ice cream or chocolate sundae.

• How many different choices are there for lunch?

Fundamental Counting Principle

• In some problems, there can be a lot of variations.

• In order to find the number of variations, we can use the Fundamental Counting Principle.

What's for lunch?

• Use the Fundamental Counting Principle to quickly determine how many options there are for lunch.

Poll

How many possible outcomes are there for an experiment in which two number cubes are rolled together?

• 6

• 36

• 12

• 18

Multiple Choice

Two number cubes are rolled once. How many possible outcomes are there for which the first roll is even and the second roll is even?

• 6

• 36

• 12

• 9

Poll

Suppose a bag contains 2 red and 4 blue marbles. I select a marble from the bag, look at it, then replace it. Then I select a second marble from the bag. How many outcomes are possible? (Treat each marble as unique: red1, red2, blue1, etc.)

• 9

• 36

• 4

Poll

Suppose a bag contains 2 red and 4 blue marbles. I select a marble from the bag. What is the probability I select a red marble?

• $$\frac{1}{3}$$  

• $$\frac{2}{3}$$

Poll

Suppose a bag contains 2 red and 4 blue marbles. I select a marble from the bag. What is the probability I select a blue marble?

• $$\frac{1}{3}$$  

• $$\frac{2}{3}$$

Poll

Suppose a bag contains 2 red and 4 blue marbles. I select a marble from the bag, look at it, then replace it. Then I select a second marble from the bag. What is the probability I select a red marble then a blue marble?

• $$\frac{2}{9}$$

• $$\frac{2}{36}$$

• $$\frac{1}{18}$$

Alphabet Cards

• I have a stack of 52 alphabet cards

• 26 uppercase cards (A, B C, . . .)

• 26 lowercase cards (a, b, c, . . .)

• What is the probability I select one card and it is an uppercase vowel?

Chipotle

• Chipotle offers a variety of choices for food. How many options are there?

• You can have a burrito, bowl, salad or tacos

• Choices for protein include carne asada, chicken, steak, barbacoa, carnitas, sofritas or veggies

Chipotle

• Choices for rice include white, brown, cauliflower or no rice

• Choices for beans include black, pinto or no beans

• Choices for salsa include fresh tomato, corn, green tomatillo, red tomatillo or no salsa

• You can also have sour cream, fajita veggies, cheese or lettuce (or not!)

Don't forget the guac!

Chipotle

• Choices for rice include white, brown, cauliflower or no rice

• Choices for beans include black, pinto or no beans

• Choices for salsa include fresh tomato, corn, green tomatillo, red tomatillo or no salsa

• You can also have sour cream, fajita veggies, cheese or lettuce (or not!)