- 1. A coin is tossed four times. How many possible sequences of heads or tails are possible?
- 2. The members of the Math Club need to elect a president and a vice president. They determine that there are a total of 272 ways that they can fill the positions with two different members. How many people are in the Math Club?
- 3. How many different 5-digit codes are
possible using the keypad shown at the right if the first digit cannot be 0 and no digit may be used more than
once?
- 4. Before 1995, area codes had the following format.
(XYZ)
X = 2, 3, . . ., or 9
Y = 0 or 1
Z = 0, 1, 2, . . ., or 9
How many area codes were possible before 1995?
- 5. Before 1995, area codes had the following format.
(XYZ)
X = 2, 3, . . ., or 9
Y = 0 or 1
Z = 0, 1, 2, . . ., or 9
, but in 1995, the restriction on the middle digit was removed, allowing any digit in that position. How many total codes were possible after this change was made?
- 6. How many ways can six different books be arranged on a shelf if one of the books is a dictionary and it must be on an end?
- 7. Ahmed has homework in, Arabic, math, chemistry, and English. How many ways can he choose the order in which to do his homework?
A) (3) X (2)
B) (4) x (3) X (2) x (1)
C) (4)x(3)
D) 4
- 8. A student is registering at a Web site. He must select a password containing six numerals to be able to use the site. How many passwords are
allowed if no digit may be used more than once?
- 9. State whether the events are independent or dependent?
Each of six people guess the total number of points scored in a basketball game. Each person writes down his or her guess without telling what it is.
- 10. State whether the events are independent or dependent?
selecting a fiction book and a nonfiction book at the library
- 11. State whether the events are independent or dependent? The letters A through Z are written on pieces of paper and placed in a jar.
Four of them are selected one after the other without replacing any of them
- 12. Ahmed wants to buy one of three different books he sees in a book store. Each is available in print and on CD. How many book and format choices does he
have?
A) (3) x (3)
B) (2) x (2) X (2)
C) (2) x (3)
D) (3) x (3) X (3)
- 13. A video store has 8 new releases this week. Each is available on videotape
and on DVD. How many ways can a customer choose a new release and a
format to rent?
- 14. Ahmed has homework in math, chemistry, and English. How many ways can he choose the order in which to do his homework?
- 15. The menu for a dinner has a choice of 2 types of salad, 5 main courses, and 3 desserts. How many ways can a salad, a main course, and a dessert be selected to form a meal?
- 16. A baseball glove manufacturer makes gloves in 4 different sizes, 3 different types by position, 2 different materials, and 2 different levels of quality. How many different gloves are possible?
- 17. Each question on a five-question multiple-choice quiz has answer choices labeled A, B, C, and D. How many different ways can a student answer the five questions?
A) (5) x (4)
B) (5) x (4) x (3) X (2) x (1)
C) (5) x (5) x (5) X (5) x (5)
D) (4) x (4) x (4) X 4) x (4)
- 18. An ice cream shop offers a choice of two types of cones and 15 flavors of ice cream. How many different 1-scoop ice cream cones can a customer order?
- 19. The ice cream shop offers 4 flavors. You order a double-scoop cone. In how many different ways can the clerk put the ice cream on the cone if you wanted two different flavors?
A) (4) x (4)
B) 1
C) (4) x (4) x (4) X (4) x (4)
D) (4) x (3) X (2) x (1)
E) (4) x (3)
- 20. State whether the events are independent or dependent?
The ice cream shop offers 4 flavors. You order a double-scoop cone. In how many different ways can the clerk put the ice cream on the cone if you wanted two different flavors?
A) Independent
B) Dependent
- 21. State whether the events are independent or dependent?
An ice cream shop offers a choice of two types of cones and 15 flavors of ice cream. How many different 1-scoop ice cream cones can a customer order?
A) Dependent
B) Independent
- 22. If the dice is rolled and then the coin is tossed. How many possible outcomes
A) 12
B) 8
- 23. How many ways can the letters of the word MATH be arranged?
A) (4) x (3)
B) (4) x (3) X (2) x (1)
C) 4
D) (4) x (4) X (4) x (4)
- 24. In how many ways; leader and vice leader can be chosen for group of 5 students? Assuming that a person can hold only one office
A) (5) x (4)
B) (5) x (2)
C) (5) x (4) x (3) X (2) x (1)
D) 2
- 25. Nine students inter classroom with 15 desks (tables). How many seating arrangements are possible if each student selects a desk?
A) 9*9*9*9*9*9*9*9*9*9*9*9*9*9*9
B) 15 * 14 *14 * 13 * 12 *11 * 10 * 9 * 8 * 7 *6 *5 * 4 * 3 *2 *1
C) 15* 9
D) 9 *8 * 7 * 6 * 5 * 4 * 3 *2 *1
E) 15 * 14 *14 * 13 * 12 *11 * 10 * 9 * 8 * 7
- 26. How many 3-letter words can be formed from the letters A, B, C and D? if each letter is used only once in each arrangement?
A) 4 *3*2 = 24
B) 4 *3=12
C) 4 *4 *4 =64
D) 2 *2 *2 *2=16
- 27. How many ways can you choose 4 different trees out of a group of 7 to plant in a row beside the street?
A) 4 * 4 * 4 * 4 * 4 * 4 * 4
B) 7 *4
C) 7 *7 *7 *7
D) 7 *6 *5 * 4
E) 7 *6 *5 * 4 * 3 *2 *1
- 28. In how many ways can four men and 3 women be seated in a raw of seven seats if the women are to be seated together in the first and then the men are to be seated together
- 29. In how many ways can five math books be placed on a shelf if 2 of them are algebra books and should be placed next to each other?
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