# 1.6: Chapter 1 Review

**At Grade**Created by: Bruce DeWItt

There are three primary counting methods that are commonly used in probability: the Fundamental Counting Principle, combinations, and permutations. The Fundamental Counting Principle states that to find the number of outcomes for a given situation, simply multiply the number of ways each event may occur by each other. When deciding whether to use combinations or permutations, you must ask if the order matters. If so, use permutations, otherwise use combinations.

When working with counting outcomes, it is often helpful to have an organizational strategy. Common strategies involve making organized lists, grids, or tree diagrams. Using these strategies will make it much easier for you to come up with the sample space.

### Chapter 1 Review Exercises

1) Suppose that two 5-sided dice are rolled.

a) Draw a grid showing all the outcomes for the different totals that may occur.

b) Use {brackets} to write down the sample space.

c) Suppose a friend offers to play a game in which you are paid $4 any time a number divisible by 4 occurs. Otherwise you pay your friend $2. If you decide to play, would you expect to win money or lose money? Use your grid from part a) to help explain your answer.

2) The lunch at The Diner has a choice of ham, turkey, or roast beef on rye or white bread with coffee or milk. Draw a tree diagram that illustrates what a person might have for lunch if they pick only one meat, one bread, and one drink.

3) Find the value for each expression below. Show your work by hand and use your calculator to verify your results.

a) 5!

b) \begin{align*}_6P_3\end{align*}

6P3

c) \begin{align*}_7C_5\end{align*}

7C5

d) (5 2)!

e) 4! 2!

4) There are four runners in a race. In how many ways can the runners finish the race?

5) A store has eighteen outfits available for a window display, but only six outfits can fit at one time in the display. In how many different ways can 6 outfits be selected?

6) Paul has three baseballs and four bats. How many possible ball and bat combinations can he choose?

7) How many license plates are possible if each plate must have three letters followed by three digits and repeats are allowed?

8) How many license plates are possible if each must have three letters followed by three digits and repeats are not allowed?

9) There are twenty candidates in the Mr. Minnesota contest. How many ways could the judges choose the winner, first-runner up, and second-runner up?

10) The yearbook editor must select two photos out of 42 juniors and two out of the 45 seniors for a page in the yearbook. How many photo combinations are possible?

11) A homeless shelter has decided to purchase all new kitchen appliances. They need one oven, one refrigerator, and one dishwasher. The appliance store has 7 brands of ovens, 6 brands of refrigerators, and 5 brands of dishwashers. In how many brand arrangements can they purchase their appliances?

12) An ice cream shop has 8 different flavors of ice cream available. How many 2-scoop cones can be made if you are allowed to have the same flavor for both scoops?

13) An ice cream shop has 8 different flavors of ice cream available. How many 2-scoop cones can be made if you decide not to have the same flavor for both scoops?

14) Suppose a jury of 12 is being selected from a pool of 20 candidates. In how many ways can this be done?

15) Suppose a jury of 12 is being selected from a pool of 13 men and 7 women. In how many ways can this be done if the judge states that the jury must contain *exactly* 5 women?

16) Suppose a jury of 12 is being selected from a pool of 13 men and 7 women. In how many ways can this be done if the judge states that the jury must contain *at least* 5 women?

17) In how many ways can I put together an outfit if I have 7 shirts, 5 pairs of pants, and 4 hats from which to choose?

18) For $7.99, a restaurant will sell you their lunch special. The special is either a hamburger or chicken sandwich, onion rings or fries, and soda or coffee.

a) Make a tree diagram showing the different ways a customer may order the lunch special.

b) How many outcomes are there? Use the Fundamental Counting Principle to justify your answer.

### Image References

Breakfast http://worldaffairspittsburgh.blogspot.com

Tetrahedral Dice http://www.bbc.co.uk

Harry Potter Books http://www.dipity.com

Ice Cream Cones http://www.bunrab.com

Raffle Ticket http://canuckamusements.com

Color Crayon http://www.rosespet.com

Exam http://www.iphlebotomycertification.com

Rep/Dem http://thyblackman.com

Rainbow http://tracynicholls.webs.com/

License Plate http://www.15q.net

Appliances http://homeappliancesblog.com/

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