Name:______________________________________________Probability and Statistics
SHOW ALL WORK, INCLUDING THE SET-UP FOR YOUR PROBLEM NEATLY.
(Unless designated, answers should be simplified fractions NOT decimals)
Permutations, Combinations, and Fundamental Counting Principal
For each problem, FIRST determine if you should use Fundamental Counting Principle (FCP),
Permutation (P)…order matters, or Combination (C)…order doesn’t matter. Check those answers
before moving on to calculate the indicated value.
1. Thirteen skiers are competing in the final round of the Olympic freestyle skiing aerial competition. In
how many different ways can the skiers finish the competition? (Assume no ties.)
2. In how many different ways can 7 skiers win the gold, silver and bronze medals?
3. The standard configuration for a New York license plate is 3 letters followed by 4 digits.
a.) How many different license plates are possible if digits and letters can be repeated?
b.) How many different license plates are possible if the first digit cannot be zero and no letters can
be repeated?
4. How many distinguishable ways can the letter of the word INTERCEPT be arranged?
5. The ambassadors have been practicing 12 songs, but here is only time for them to perform 5 of them in
the spring concert. How many different ways can they select 5 songs to perform?
6. CHS can send 2 representatives from the Math Bowl team to the state competition. If there 18 people on the
team, how many ways can they choose the 2 representatives?
7. You must take 6 elective classes to meet your graduation requirements for college. There are 12 classes that
you are interested in. In how many ways can you select your elective classes?
8. A restaurant serves omelets that can be ordered with any of the following ingredients:
Vegetarian toppings – Green pepper, Red pepper, Onion, Mushroom, Tomato, Cheese
Meat – Ham, Bacon, Sausage, Chicken,
Suppose you want exactly 2 vegetarian ingredients and 1 meat ingredient in your omelet. How many different
types of omelets can you order?
9. Find the number of possible 5-card hands that contain 5 face cards (either kings, queens, or jacks.)
10. How many different ways can 4 friends stand in a cafeteria line?
11. A school shirt is available either long-sleeved or short-sleeved, in sizes small, medium, large or extra large,
and in one of two colors. How many different choices for a school shirt are there?
12. “Ringing the changes” is a process where the bells in a tower are rung in all possible ways. Westminster
Abbey has 10 bells in its tower. In how many ways can its bells be rung?
Probability
13. A fruit bowl contains 4 green apples and 7 red apples. What is the probability that a randomly selected apple
will be green?
14. When two number cubes labeled 1-6 are rolled, what is the probability that the result will be two 4’s?
15. Tom has a dollar’s worth of dimes and a dollar’s worth of nickels in his pocket.
a.) What is the probability he will randomly select a dime from his pocket?
b.) What is the probability he will randomly select a nickel from his pocket?
16. The police department gathers statistics on Tuesday. Officers count a total of 608 vehicles, of which 380
go straight through the intersection, 76 turn north and the rest turn south.
a.) What is the probability that a vehicle will turn north?
b.) What is the probability that a vehicle will turn north or go straight through the intersection?
c.) What is the probability that a vehicle will not turn north?
17. Find the probability of randomly selecting a red disk in one draw from a container that contains
2 red disks, 4 blue disks, and 3 yellow disks.
18. Find the probability of randomly selecting an orange marble in one draw from a jar containing
8 blue marbles, 5 red marbles and 2 orange marbles.
19. A market research firm conducted a survey of 250 customers of longdistance carrier A and 250 customers of long-distance carrier B. The
customers were asked whether they were satisfied with, dissatisfied with, or
had no opinion about their long-distance service. The responses are recorded
in the following chart:
a.)Find the probability that a randomly selected respondent to the survey is satisfied with or has no opinion about
their long-distance service
b.) Find the probability that a randomly selected respondent to the survey is a customer of long-distance carrier B
or is satisfied with the long-distance service.
20. Demographics: (Good time to use percents)
The table below shows the 1993 college enrollment statistics, in thousands for the United States. Bases on this data,
find the probability that a randomly selected person enrolled in college in the United States in 1993 is the indicated
group. Write your answers using percents. Round to tenths.
18-24________ 25-29 or female________ 30-34 and male________ 30 & over and female________
21. In a survey about a change in public policy, 100 people were asked if they favor the change, oppose the change,
or have no opinion about the change. The responses are indicated
at the right.
a.) Find the probability that a randomly selected respondent to the
survey opposes or has no opinion about the change in policy.
b.) Find the probability that a randomly selected respondent to the
survey is a man or opposes the change in policy