# HELP IN MATH

HELP

PERMUTATIONS/COMBINATIONS

1. Some Oregon license plates have 3 letters followed by three numbers. How many license plates are possible using this configuration of numbers and letters?

2. A local pizzeria offers 3 choices of salad, 10 kinds of pizza, and 4 different desserts. How many different three-course meals can be ordered? (Assume you will choose one each of salad, pizza and dessert.)

3. Radio stations in the United States have call letters that begin with either K or W. (Like KGW,WKRB) some have a total of three letters, while others have four letters. How many sets of three-letter call letters are possible? How many sets of four-letter call letters are possible?

4. Find the number of ways to arrange the letters in the following words.

a. OREGON b. CONCORDIA c. MISSISSIPPI

5. Students at Concordia are involved in a contest to see who can bring in the most money for service projects. Ten Freshmen, 4 Sophomores, 5 Juniors and 8 Seniors are entered. If we consider only class status, in how many ways can the winners be chosen?

6. How many different four-digit numbers can be formed from the digits 1,2,3,4,5,6,7, and 8? Each digit can only be used once.

7. If 10 horses are entered in an upcoming meet, how many ways can the first three places be determined?

8. Thirty students enter a contest offering scholarships to the first and second place winners. In how many ways can the two winners be chosen from the 30 students?

9. Julie wants to select a committee of 3 to represent the Math 110 students in a math competition. If there are 34 students in the two sections, in how many ways can these students be chosen?

10. A basketball coach was criticized by parents for not trying out every combination of players. If the team roster has 12 players, how many 5-player combinations are possible?

11. A disc jockey can play eight records in a 30-minute segment of her show. For a particular 30-minute segment, she has 12 records to select from. In how many ways can she arrange he program for the particular segment?

12. A newspaper boy discovers in delivering his papers that his is three papers short. He has eight houses left to deliver to, but only five papers left. In how many ways can he deliver the remaining newspapers?

13. A committee of 11 people, six women and five men, is forming a subcommittee that is to be made up of two women and three men. In how many ways can the subcommittee by formed?

14. Assume a class has 18 members.

a. In how many ways can a president, vice-president and secretary be selected?

b. How many committees of three persons can be chosen?

*15 . In how many ways can 5 couples be seated in a row of 10 chairs if no couple is separated?

HELP 2

PROBABILITY

1. A dog owner has 2 beagles, 2 golden retrievers and one cocker spaniel. If two of these dogs are randomly selected, determine the following:

a. List the sample space of this experiment

b. What is the probability of selecting 2 dogs of the same type?

2. An experiment consists of tossing two ordinary dice and adding the two numbers. Determine the probability of obtaining:

a. A sum of 8 b. A sum less than or equal to 4 c. A sum greater than 7

3. Draw a probability tree for the following experiment:

Choosing an M&M from a bowl containing one each of an orange, red, blue, yellow, brown and green M&M and then having either a Coke or a Pepsi.

4. If an experiment consists of spinning Spinner A

and then spinning Spinner B, Red

Blue Pink Red

Purple

a. What is the probability of spinning blue then red? Red Pink

b. What is the probability of spinning purple then pink? Spinner A Spinner B

5. 12 regular playing cards having 5 hearts, 4 clubs, and 3 diamonds are shuffled and placed face down on the table. Determine the probability of selecting 2 clubs if:

a. The first card selected IS returned to the table for the second selection. (An independent

b. The first card selected is NOT returned to the table for the second selection. (A

dependent event)

6. A young child is given 9 uncolored geometric wooden pieces of approximately the same size: 3 triangular shaped, 3 square shaped, and 3 hexagonal shaped. The pieces are mixed up in a box and the child selects 3 hexagonal shaped pieces without replacement. The parent wonders if the child can distinguish between the hexagonal pieces and the other pieces, of if this was accidental.

a. If such a selection is done randomly (selected one at a time), what is the probability to the nearest tenth of a percent of obtaining 3 hexagonal shapes from the 9 pieces?

b. Does the evidence suggest that the child can distinguish the hexagonal shape from the 9 pieces?

7. If a person is randomly selected from the U.S. population, the odds the person lives in California are 1 to 8.

a. What is the probability of a randomly chosen person being from California?

b. What are the odds of a randomly chosen person not being from California?

8. A certain sweepstake ticket has four categories of prizes with the following probabilities of being

PRIZE VALUE PROBABILITY

$100,000 1/500,000

$ 50,000 1/250,000

$ 20,000 1/200,000

$ 10,000 1/100,000

a. What is the expected value of buying these sweepstakes tickets?

b. If each ticket is $1, is this a fair contest? (Why/why not?)