# Combinations, permutations, and mutual exclusivity

1. A husband and wife want to purchase wallpaper for their living room and paint for their kitchen. If they can choose from six different wallpaper patterns and ten different colors of paint, how many possible outcomes from this sequence of events do they have available?

720

16

7200

60

2. An inspector selects four batteries from a lot and then tests each battery to see whether it is overcharged, normal, or undercharged. How many possible outcomes are there? 7

12

27

64

3. If a Little League baseball manager has two pitchers and four catchers, how many different pitcher-catcher arrangements does he have for his forthcoming game?

2

6

8

10

4. How many different committees of five people can be formed from nine available persons?

14

45

126

15,120

5. How many different three-letter nonsense syllables can be formed from the letters of the word "pilot," if repetitions are not allowed?

60

125

150

210

6. If there are 100 tickets sold for a raffle and one person buys 12 tickets, what is the probability of that person winning the prize?

0.88

0.50

0.40

0.12

7. A pair of octagonal dice, each with faces marked 1 through 8, are tossed in succession. What is the probability of a sum greater than 14 showing on the upturned faces?

0.0469

0.0625

0.0781

0.0938

8. If two events are known to be mutually exclusive, what do you know about them?

They are dependent.

They are independent.

Their joint probability can exceed 1.

Their joint probability is close to 0.

9. At a firefighters' fund raiser, citizens of three committees are in attendance. There are 18 from Camp Hill, 21 from West Town, and 32 from East Wilson. If a person is selected at random, what is the probability that the chosen individual is not from West Town?

0.296

0.549

0.704

0.746

10. Twenty-two girls are taking home economics at Beaver Hill High School. Six say they want to learn how to make ceramic figurines for their home, eleven say they want to learn how to cook, and five say they want to learn how to sew. If one of these students is selected at random, what is the probability that she wants to learn ceramics?

0.727

0.549

0.227

0.273

11. What is the probability that, given an ordinary deck of 52 playing cards, a person randomly draws the 9 of clubs, replaces it, and then draws the queen of hearts?

0.020

0.019

0.000377

0.000370

12. What is the probability that, given an ordinary deck of 52 playing cards, a person randomly draws the ace of diamonds or a red card?

0.500

0.250

0.212

0.200

13. The probability of a tourist visiting the White House is 0.75 and the probability of visiting the Capitol is 0.60. The probability of visiting both places on the same day is 0.48. Find the probability that a tourist visits the White House or the Capitol.

0.87

0.93

0.99

1.35

14. A small consulting firm employs secretaries, financial analysts, research assistants, and computer programmer/analysts. The distribution of employees according to full-time or part-time status is shown in the table below.

Secretaries Financial Analysts Research Assistants Computer Programmer/Analysts TOTAL

Full-Time 3 1 2 4

Part-Time 2 1 3 2

TOTAL

If an employee is selected at random, what is the probability that the person is a part-time employee, given that the selected individual is a research assistant?

0.600

0.278

0.167

0.111

15. Suppose it is known that 68 % of all American taxpayers enjoy watching old black-and-white movies. If you selected three American taxpayers at random from a computer database of all American taxpayers, what is the probability that at least one enjoys old black-and-white movies?

0.0328

0.227

0.314

0.967

16. A scientific poll found that 54% of the American people want the United States to develop hydrogen fuel alternative energy. If six people are selected at random, find the probability that these six Americans favor this alternative means of energy.

15.7%

8.5%

4.6%

2.5%

17. How many different ways can a student select 3 electives from a list of 12 electives?

1320

220

72

36

18. How many different 4-digit identification badges can be made, if the first digit must be 9 and the other digits can be used more than once?

6561

5040

729

126

19. At a large university 64.8% of the students own lap-top computers. If four students are randomly selected, find the probability that none own a lap-top computer.

.0154

.1763

.2189

.8237

20. A video store has 12 DVD movies and 4 VHS movies on sale. If two customers purchased a movie, find the probability that one of each type of medium for a movie was purchased.

0.25

0.75

0.40

0.80

#### Solution Summary

Various statistics problems on probabilities, combinations, permutations and mutual exclusivity.