Tree Diagrams and Counting Principle Review
1.You have a photo that you want to mat and frame. You can choose from a blue, purple, red, or green mat and a metal or wood frame. Use a tree diagram to show all the possible frames you can have made.
2.The 5-digit zip code system for United States mail was implemented in 1963. How many different possibilities of zip codes are there with a 5-digit zip code where each digit can be 0 through 9?
3.How many different phone numbers are possible using a 3-digit area code and a 7-digit phone number if the first digit of the area code and phone number cannot be zero?
A 3,486,784,401 C 9,500,000,000
B 8,100,000,000 D 10,000,000,000
4.Mrs. Sharpe is planning her dinners for next week. The choices
for the entree are roast beef, turkey, or pork. The choices of
carbohydrates are mashed potatoes, baked potatoes, or noodles. The vegetable choices are broccoli, spinach, or carrots. Make a tree diagram indicating the possible outcomes for a meal that includes a meat, a carbohydrate and a vegetable.
5.Mitch bought 2 sports magazines, 3 guitar magazines, and 3 news magazines. How many choices of magazines does he have to read?
6.Sarah needs to register for one course in each of the six subject areas. The school offers 5 math courses, 4 foreign language courses, 3 science courses, 3 English courses, 5 social studies courses, and 6 elective courses. In how many ways can she register?
7.License plates are being produced that have a single letter followed by three digits. All license plates are equally likely. Find the number of possible license plates.
8.Social Security numbers contain 9 digits. All social security numbers are equally likely. Find the number of possible Social Security numbers.
9.A lunch menu consists of 3 types of sandwiches, 2 types of soup, and 3 types of fruit. A student wants to order one sandwich, one bowl of soup, and one piece of fruit. How many different lunches are possible?
10.A baker can make yellow or white cakes with a choice of chocolate, strawberry, or vanilla icing. Describe all of the possible combinations of cakes using a tree diagram.
11.Personal identification numbers (PINs) contain 2 letters followed by 4 digits. Assume that all codes are equally likely. Find the number of possible PINs.
12.You want to buy a new i-Pod. You can choose from a nano, shuffle, or video. They come in white, black, pink, and blue. List all of the
i-Pods sold by drawing a tree diagram.