Answer Each Question Completely. SHOW YOUR WORK

Name: ______

Date: ______

Answer each question completely. SHOW YOUR WORK !!

1.Evaluate. Show your work using factorials.

a.1a. ______

b.1b. ______

2.Solve for n:2. ______

3.Use the Binomial Theorem to expand and simplify the expression:

4.Use the Binomial Theorem to expand and simplify the expression:

5.Find the coefficient a of the term in the expansion of the binomial.

BinomialTerm

5. ______

6.Slips of paper numbered 1 through 14 are placed in a hat. In how many ways can you draw two numbers with replacement that total 12?

6. ______

7.A customer in an electronics store can choose one of six speaker systems, one of five DVD players, and one of six plasma televisions to design a home theater system. How many systems can be designed?

7. ______

8.The same three-digit prefix is used for all of the telephone numbers in a small town. How many different telephone numbers are possible by changing only the last four digits?

8. ______

9.There are 10 bicyclists entered in a race. In how many different ways could the top three places be decided?

9. ______

10.A group of potential jurors has been narrowed down to 32 people. In how many ways can a jury of 12 people be selected?

10. ______

11.Find the number of diagonals of a regular 15-sided polygon. A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.

11. ______

12.Eight people are going for a ride in a boat that seats eight people. The owner of the boat will drive, and only three of the remaining people are willing to ride in the two bow seats. How many seating arrangements are possible?

12. ______

13.a. Determine the number of permutations of all the letters in the word:

LOGARITHM

13a. ______

b. How many of these permutations begin with L and end with M?

13b. ______

14.a. Determine the number of distinguishable permutations of all the letters in the word:

ESTIMATE.

14. ______

15.In a class of 30 students, it is found that 22 play soccer, 18 play baseball (or

softball), and 5 play neither sport.

a. How many students play both sports? 15a. ______

b. How many students play soccer, but

not baseball (or softball)? 15b. ______

16.Consider a raffle in which the digits 3, 4, and 5 are written on three separate slips of paper and placed in a box. Three digits are then drawn randomly one at a time, with replacement, and the digits appearing on the slips are written down from left to right in the order in which they are drawn.

a. Write out the sample space of possible 3-digit numbers.

b. What is the probability that the 3-digit number is an odd number?16b. ______

17.Find the probability for the experiment of tossing a six-sided die twice such that the sum is a multiple of 3.

17. ______

18.Find the probability for the experiment of selecting one card from a standard deck of 52 playing cards such that the card is a face card or a deuce (a “deuce” is a 2).

18. ______

19.Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing four green, five yellow, and two red marbles such that the marbles are yellow.

19. ______

20.A man has five pairs of socks, of which no two pairs are the same color. He randomly selects two socks from a drawer. What is the probability that he gets a matched pair?

20. ______

21.In a shipment of 40computer chips, 5 are known to be defective.

If 20 of these computer chips are selected at random, what is the probability that

at least 3 in the selection are defective? Round to the nearest thousandth.

21. ______

22.You attend a karaoke night and hope to hear your favorite song. The karaoke song book has 300 different songs (your favorite song is among the 300 songs). Assuming that the singers are equally likely to pick any song and no song is repeated, what is the probability that your favorite song is one of the 20 that you hear that night?

22. ______

23.A card is drawn at random from a standard deck of 52 playing cards. Determine

whether the indicated events are complementary, mutually exclusive but not

complementary, or not mutually exclusive.

a. A: The first card drawn is a jack.23a. ______

B: The first card drawn is a diamond. ______

b. C: The first card drawn is a heart.23b. ______

D: The first card drawn is a club. ______

24.Suppose in one class of students, 55% of the students are male, 35% of the students wear glasses or contacts, and 21% of the students are males who wear glasses or contacts. Are gender and corrective eyewear independent? Justify your answer.

24. ______