Counting Principle and Combinations

The cafeteria has 2 choices of salads, 3 choices of entrees, and 2 choices of beverages. How many meal combinations are available and why?

• 7 because 2 + 3 + 2

• 12 because 2 x 3 x 2

A radio host plans to play one song from each of 3 CDs by a single artist.  The first CD includes 12 songs.  the second CD includes 14 songs, and the third includes 13 songs.  How many different combinations are possible?

• 39

• 2184

• 117

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

• 15

• 40

• 80

• 10

At  a New Car Dealership a particular model comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?

• 180

• 23

• 12

• 60

At Papa John's you are deciding on what you want for dinner. The pizza offers 8 different meats, 4 different cheeses, 3 different crust types and 2 different sauces. How many different pizzas do you have to choose from?

• 32

• 192

• 40,320

• 51,200

A menu has 6 different sandwiches, with 3 choices of potato chips, 3 types of salad and 5 different beverages. How many different lunch combinations consisting of a sandwich, chips and beverage can be ordered?

• 30

• 17

• 90

• 270

Jacob is choosing an outfit from three pairs of jeans and three shirts.  The jeans are blue, black, and gray.  The shirts are white, blue, and yellow.  How many such outfits are possible?

• 3

• 6

• 9

The student council is selling sweatshirts with the school name and emblem.  The shirts come in colors, styles, and sizes.  There are 3 colors (white, gray, black); 2 styles (hooded, crew); and 3 sizes (small, medium, large).  How many different types of sweatshirts are available?

• 11

• 18

• 9

A student can choose one sandwich, one salad,  and one piece of fruit in the cafeteria.  The choices include the following: grilled cheese sandwich, hamburger, tuna sandwich, garden salad, fruit salad, apple, banana, and orange.  How many different lunches are possible?

• 18

• 8

• 24

Members of a video club choose a personal identification number (PIN) consisting of 2 letters followed by 2 digits.  How many PIN's are possible if letters and digits are repeated? 

• 67, 600

• 72

• 1, 000, 000