Deck 12: The Nature of Counting

Question 1

Let R, F, L, B, T, U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Name the move or moves that will return the cube to standard position after making the move B^-1. ​

A) F²
B) B²
C) B⁴
D) (B^-1)²
E) B

Answer 1

B

Question 2

Let R, F, L, B, T, U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Name the move that will return the cube to standard position after making the move BF^-1.

Answer 2

FB^-1

Question 3

Name the move on Rubik's Cube that will return the cube to standard position after making the move R. ​

A) B^-1
B) R²
C) R^-1
D) BR
E) R³

Answer 3

R^-1

Question 4

Instant Insanity has 331,776 possibilities (not all different). Suppose a computer could print out 1000 arrangements every four seconds. How long would it take for this computer to print out all possibilities? ​

A) 13 minutes, 28 seconds
B) 9 minutes, 13 seconds
C) 11 minutes, 9 seconds
D) 22 minutes, 7 seconds
E) 2 hours, 22 minutes, 7 seconds

Question 5

Let R, F, L, B, T, U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Name the move on Rubik's Cube that will return the cube to standard position after making the move ​L.

Question 6

R, F, L, B, T, U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Name the move that will return the Rubik Cube to standard position after making the move T².

Question 7

Let R, F, L, B, T, U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Name the move that will return the cube to standard position after making the move BU.

Question 8

Instant Insanity has 331,776 possibilities (not all different). If you could make one different move per four seconds, how long do you think it would take you to go through all these arrangements?
​
It would take __________ days, __________ hours, __________ minutes, __________ seconds.

Question 9

Name the move or moves that will return the Rubik Cube to standard position after making the move L². ​

A) BL
B) LB
C) L²
D) L^-2
E) L⁴

Question 10

Let R, F, L, B, T, U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Name the move that will return the cube to standard position after making the move L³.

Question 11

Let R, F, L, B, T, U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Name the move that will return the cube to standard position after making the move T^-1F^-1. ​

A) FT
B) TF²
C) TF
D) F(T^-1)³
E) T²F²

Question 12

Instant Insanity has 331,776 possibilities (not all different). If you could make one different move per two seconds, how long do you think it would take you to go through all these arrangements? ​

A) 7 days, 16 hours, 19 minutes, 12 seconds
B) 16 days, 10 hours, 10 minutes, 26 seconds
C) 3 days, 6 hours, 10 minutes, 26 seconds
D) 6 days, 10 hours, 10 minutes, 26 seconds
E) 3 days, 6 hours, 18 minutes, 20 seconds

Question 13

Let R, F, L, B, T, U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Name the move or moves that will return the cube to standard position after making the move RF. ​

A) F^-1R^-1
B) R^-1F^-1
C) ​FR³
D) ​R²F²
E) ​FR²

Question 14

Let R, F, L, B, T, U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Name the move that will return the cube to standard position after making the move U^-1.

Question 15

Show the result of the moves on Rubik's cube FT​ ^-1. Remember that R, F, L, B, T, and U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Use the standard Rubik's cube shown below as your starting point. Consider each clockwise rotation by first turning the cube so that the side you are rotating is facing you. ​ ​

A)
B)
C)
D)
E)

Question 16

Let R, F, L, B, T, U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Name the move that will return the cube to standard position after making the move R^-1U^-1.

Question 17

Let R, F, L, B, T, U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Name the move that will return the cube to standard position after making the move BU^-1. ​

A) UB
B) U^-1B
C) BU²
D) B²U²
E) UB^-1

Question 18

Let R, F, L, B, T, U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Name the move or moves that will return the cube to standard position after making the move R³. ​

A) TR³
B) RT²
C) R⁴
D) (R^-1)³
E) R

Question 19

Show the result of the moves on Rubik's cube U³. Remember that R, F, L, B, T, and U mean rotate 90° clockwise the right, front, left, back, top, and under faces, respectively. Use the standard Rubik's cube shown below as your starting point. Consider each clockwise rotation by first turning the cube so that the side you are rotating is facing you. ​ ​

A)
B)
C)
D)
E)

Question 20

Instant Insanity has 331,776 possibilities (not all different). Suppose a computer could print out 1000 arrangements every four seconds. How long would it take for this computer to print out all possibilities?
​
It would take __________ days, __________ hours, __________ minutes, __________ seconds.

Question 21

The old lady jumping rope in the cartoon at the figure below is counting one at a time. Assume that she jumps the rope 55 times per minute and that she jumps 6 hours a day, 4 days a week, 30 weeks a year. Estimate the length of time necessary for her to jump the rope the number of times indicated in the cartoon. Round the answer to one decimal place.
​ ​
__________ centuries

Question 22

Suppose a restaurant offers the prix fixe menu below.
​
Main course: prime rib, steak, chicken
Side dish: soup, salad, crab cakes
Dessert: cheesecake, chocolate delight, ice cream
Beverage: coffee, tea, milk
​
In how many ways can someone order a meal consisting of one choice from each category?

Question 23

You flip a coin three times and keep a record of the results. In how many ways could you obtain at least one tail? ​

A) 4
B) 11
C) 9
D) 8
E) 7

Question 24

​There are five boys and five girls at a party. In how many ways can they be seated in a row of six? ​

A) ​720
B) ​5
C) ​151,200
D) ​210
E) ​120

Question 25

Evaluate the expression. ​ ​

A) 73
B) 63
C) 75
D) 70
E) 68

Question 26

There are four boys and four girls at a party. In how many ways can they be seated in a row of five?

Question 27

Jean Sherrod of Little Caesar's Enterprises, Inc., explains that an order where the first pizza is pepperoni and the second pizza is ham would be considered different from an order in which the first pizza is ham and the second pizza is pepperoni. Using this scheme, how many pizza orders are possible?
​

Question 28

You flip a coin six times and keep a record of the results. In how many ways could you obtain at least two tail?

Question 29

A city license plates consist of three letters followed by three numerals. Suppose 246 letter arrangements are not allowed. How many plates can New York issue?

Question 30

A night watchman visits 8 offices every night. To prevent others from knowing when he will be at a particular office, he varies the order of his visits. In how many ways can this be done?​ ​

A) ​20,160
B) ​8
C) ​1
D) ​5,040
E) ​40,320

Question 31

Suppose a restaurant offers the following prix fixe shown below. ​
Main course: prime rib, steak, chicken
Side dish: soup, salad, crab cakes
Dessert: cheesecake, chocolate delight0
​Bevarage: ​coffee, tea, milk
​
In how many ways can someone order a meal consisting of one choice from each category?
​

A) 36
B) 72
C) 47
D) 18
E) 54

Question 32

A typical Social Security number is 555-47-5593. How many Social Security numbers are possible if the first two digits cannot be 3?​

A) 810,000,000
B) 490,000,000
C) 900,000,000
D) 640,000,000
E) 729,000,000

Question 33

A night watchman visits 9 offices every night. To prevent others from knowing when he will be at a particular office, he varies the order of his visits. In how many ways can this be done?

Question 34

Evaluate the expression. ​ ​

A)
B)
C)
D)
E)

Question 35

In how many ways can four taxi drivers be assigned to eight cars? ​

A) 5,040
B) 70
C) 3,024
D) 126
E) 1,680

Question 36

Jean Sherrod of Little Caesar's Enterprises, Inc., explains that an order where the first pizza is pepperoni and the second pizza is ham would be considered different from an order in which the first pizza is ham and the second pizza is pepperoni. Using this scheme, how many pizza orders are possible? ​ ​

A) 88,059,456
B) 88,378,801
C) 88,397,604
D) 88,407,604
E) 88,347,604

Question 37

The old lady jumping rope in the cartoon at the figure below is counting one at a time. Assume that she jumps the rope 50 times per minute and that she jumps 7 hours a day, 4 days a week, 30 weeks a year. Estimate the length of time necessary for her to jump the rope the number of times indicated in the cartoon. ​ ​

A) 21,748.6 centuries
B) 21,750.1 centuries
C) 21,747.1 centuries
D) 21,748.1 centuries
E) 21,748.2 centuries

Question 38

A typical Social Security number is 555-47-5593. How many Social Security numbers are possible if the first three digits cannot be 1?

Question 39

In how many ways can four taxi drivers be assigned to seven cars?

Question 40

A city license plates consist of three letters followed by three numerals. Suppose 250 letter arrangements are not allowed. How many plates can New York issue? ​

A) 17,576,000
B) 17,326,000
C) 17,576,250
D) 15,818,150
E) 15,818,650

Question 41

In how many ways can you be dealt four cards from an ordinary deck of 52 cards? ​

A) 269,286
B) 270,725
C) 271,668
D) 270,735
E) 269,450

Question 42

A club consists of 16 men and 17 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people? ​

A) 596,387,610,000
B) 1,022,862,306,928
C) 563,336,193,420
D) 498,094,571,520
E) 466,507,641,600

Question 43

Evaluate the expression.
​

Question 44

How many different subsets can be chosen from a set of seven elements? ​

A)
B)
C)
D)
E)

Question 45

In how many ways can you be dealt three cards from an ordinary deck of 52 cards?

Question 46

In how many ways can a full house of three jacks and two tens be obtained?

Question 47

An ice cream parlor has 34 different flavors. A super sundae allows a person to select 3 different flavors and 3 (out of 9) different toppings. How many different selections are possible?
​
Round amount to the nearest whole number.

Question 48

Evaluate the expression.
​

Question 49

In how many ways can a full house of three jacks and two tens be obtained? ​

A) 10
B) 24
C) 28
D) 32
E) 6

Question 50

Evaluate the expression. ​ ​
​

A) 95
B) 98
C) 94
D) 96
E) 100

Question 51

In how many ways can a diamond flush be obtained?

Question 52

Tom is leading a workshop for 23 people. He wants each person to meet every other person (shake hands once). How many handshakes occur?

Question 53

Evaluate the expression. ​ ​

A) 216
B) 48
C) 576
D) 168
E) 288

Question 54

A club consists of 17 men and 18 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people?
​
Round amount to the nearest whole number.

Question 55

An ice cream parlor has 33 different flavors. A super sundae allows a person to select 4 different flavors and 4 (out of 8) different toppings. How many different selections are possible? ​

A) 2,864,400
B) 971,890,920
C) 1,649,894,400
D) 68,745,600
E) 117,600

Question 56

Evaluate the expression.
​

Question 57

How many different subsets can be chosen from a set of eight elements?

Question 58

Evaluate the expression. ​ ​

A) 154,431
B) 154,440
C) 154,433
D) 154,438
E) 154,437

Question 59

In how many ways can a club flush be obtained? ​

A) 154,440
B) 1,287
C) 2,598,764
D) 2,475,391
E) 1,382

Question 60

Tom is leading a workshop for 15 people. He wants each person to meet every other person (shake hands once). How many handshakes occur? ​

A) 213
B) 105
C) 98
D) 210
E) 108

Question 61

How many outfits consisting of a suit and a tie can a man select if he has three suits and eight ties?

Question 62

Evaluate the expression.
​

Question 63

Evaluate the expression.
​

Question 64

Evaluate the expression. ​ ​

A)
B)
C)
D)
E)

Question 65

How many eight-digit telephone numbers are possible if the first two digits cannot be twos or zeros?

Question 66

How many permutations are there of the word? ​
ESCHEW
​

A) 350
B) 570
C) 380
D) 180
E) 360

Question 67

How many permutations are there of the word?
​
ANNEX

Question 68

Evaluate the expression.
​

Question 69

Evaluate the expression. ​ ​

A)
B)
C)
D)
E)

Question 70

How many outfits consisting of a suit and a tie can a man select if he has three suits and eight ties? ​

A) 24
B) 27
C) 32
D) 21
E) 16

Question 71

Evaluate the expression.
​

Question 72

Evaluate the expression.
​

Question 73

How many permutations are there of the word?
​
GRAMMATICAL

Question 74

Evaluate the expression. ​ ​

A) 1,671
B) 1,673
C) 1,672
D) 1,680
E) 1,677

Question 75

Evaluate the expression. ​ ​

A) 40,316
B) 40,305
C) 40,315
D) 40,320
E) 40,312

Question 76

How many permutations are there of the word? ​
BOOKKEEPING
​

A) 4,989,800
B) 4,989,600
C) 2,494,800
D) 4,989,400
E) 7,484,700

Question 77

Evaluate the expression.
​

Question 78

How many seven-digit telephone numbers are possible if the first two digits cannot be twos or zeros? ​

A) 6,400,000
B) 64,000,000
C) 10,000,000
D) 8,000,000
E) 800,000