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Mathematics
8th -
11thgrade
Counting Principle/Permutations and Combinations
31 questions
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- 1. Multiple Choice
Melanie is taking four classes this semester: American History, Algebra 2, AP English, and Chemistry. How many ways can these four classes be arranged on her schedule?
24
153
765
824
- 2. Multiple Choice
An internet passcode consists of a digit followed by a letter, followed by another digit. Assuming the digits are 0-9. How many different passcodes are possible?
6,200
4,000
2,600
8,000
- 3. Multiple ChoiceWhich line is longer?TopBottomSame
- 4. Multiple Choice
Grant is rolling a standard six-sided number die eight times. How many outcomes are possible?
5,879,626
6,579,598
1,679
1,679,616
- 5. Multiple Choice
A quiz has eight multiple choice questions with four options for each (A, B, C, and D). How many ways are there to answer the questions?
48 = 65,536
84 = 4,096
4! = 24
8! = 40,320
- 6. Multiple ChoiceWhat way do the arrows point?LeftRightUpLeft and right
- 7. Multiple Choice
20P4
6,435
720
116,280
80,730
- 8. Multiple Choice
15C8
96
.003
95,361
6,435
- 9. Multiple Choice
17P7
98,017,920
5,760
765,932
36,864,440
- 10. Multiple Choice
There are 5 apples and you take 3. How many apples do you have?
5
3
2
0
- 11. Multiple Choice
27C22
35,412
80,739
2,600
24
- 12. Multiple Choice
Scott has 7 chores to complete this Saturday. How many ways can he arrange the order in which he does them?
Combination
Permutation
- 13. Multiple Choice
How many months have 28 days?
all of them
1
February
What about leap years?
- 14. Multiple Choice
There are 16 different colored markers in the bucket. How many ways can Kelly choose five of them?
Combination
Permutation
- 15. Multiple Choice
How many ways are there to elect a President, Vice President, Secretary, and Treasurer, from a club with 32 members?
Combination
Permutation
- 16. Multiple Choice
What is heavier 100kg of gold or 100 kg of feathers?
gold
feathers
they are both the same
What if the scale is incorrect?
- 17. Multiple Choice
The dance company is choosing 3 new dancers from a group of 25 who try out. How many ways can they choose the new dancers?
Combination
Permutation
- 18. Multiple Choice
There are ten toppings available to make an ice cream sundae. How many ways can Max choose two?
Combination
Permutation
- 19. Multiple ChoiceJohnny's mother had three children. The first was named April. The second child was named May. What was the third child's name?JuneJulyMarchNone of these
- 20. Multiple Choice
How many different 11-letter arrangements can be made using the letters in the word FIRECRACKER?
4,368
1,538,990
789,432
1,663,200
- 21. Multiple Choice
Mindy is purchasing songs from an album on iTunes. If the album has 14 songs, how many ways can she choose 6?
3,003
5,040
325
7,845
- 22. Multiple Choice
In which sport do 2 or 4 people hold ping-pong paddles, and play tennis on a tennis court, with a ping-pong ball?
basketball
tennis
pickleball
ping-pong
- 23. Multiple Choice
Carl is choosing a four-character password for his cell phone. The password can contain letters and digits only, and can’t include repeating characters. How many passwords are possible?
9,549
124
1,413,720
79,390
- 24. Multiple Choice
Mr. Pratt has 26 students in his math class. He has three prizes to give away: a pencil, an eraser, and a no homework coupon. How many ways can he choose three students to win these awards?
6,000
387
12,427,902
15,600
- 25. Multiple Choice
How many ways are there to choose seven cards from a deck of 52?
133,784,560
784,560
41,957
18
- 26. Multiple Choice
At your favorite restaurant you must choose 1 main course(steak, chicken, or vegetarian), 2 sides(fries, salad, mashed potatoes, corn, or broccoli), and 1 dessert(creme brulee, cheese cake, or brownies). How many different orders are there if you CANNOT choose the same 2 sides.
724
422
180
476
- 27. Multiple ChoiceA team of 8 basketball players needs to choose a captain and co-captain.64561540,320
- 28. Multiple ChoiceA group of 25 people are going to run a race. The top 8 finishers advance to the finals.2004.3609 x 101001,081,575
- 29. Multiple ChoiceYou go to Best Buy to purchase a new television. You have the following choices: LCD or plasma; screen size 27”, 32”, 36”, 41”, 51”, or 63” and manufacturer Sony, Vizio or Phillips. How many different televisions does the store have to offer?189907236
- 30. Multiple ChoiceWhen does the order in which you are choose not matter?CombiniationPermutation
- 31. Multiple ChoiceWhen does the order in which you are choose matter?CombinationPermutation
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