CH 10 review quiz

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Consider only the smallest individual cubes and assume solid stacks​ (no gaps). Determine the number of cubes in the stack shown on the right that are not visible from the perspective shown.

Cubes not visible 10

Ethel​'s collection of eleven albums includes one jazz album. Ethel will choose five of her albums to play on a road trip.​ (Assume order is not​ important.) ​a) How many different sets of five albums could she​ choose? ​b) How many of these sets would not include the jazz ​album? ​c) How many of them would include the jazz ​album?

a) Ethel can choose from __462_ different sets of albums. ​b) There are _252__ sets that would not include the jazz album. ​c) There are __210___ sets that would include the jazz album.

Cathy​'s collection of twelve albums includes one rock album. Cathy will choose four of her albums to play on a road trip.​ (Assume order is not​ important.) ​a) How many different sets of four albums could she​ choose? ​b) How many of these sets would not include the rock album? ​c) How many of them would include the rock ​album?

a=495 b=330 c=165

Find the number of combinations​ (subsets) of 10 things taken 6 at a time.

the answer is 210 combinations

Pamela​ DeMar's computer printer allows for optional settings with a panel of 4 ​on-off switches in a row. How many different settings can she select if no two adjacent switches can both be​ on?

8

A line segment joins the points ​(8,12​) and ​(73​,357​) in the Cartesian plane. Including its​ endpoints, how many lattice points does this line segment​ contain? (A lattice point is a point with integer​ coordinates.)

6

After rolling the first ball of a frame in a game of​ 10-pin bowling, how many different pin configurations can remain​ (assuming all configurations are physically​ possible)?

1024 (8x8x8x2)

​Uniform-length matchsticks are used to build a rectangular grid as shown here. If the grid is 11 matchsticks high and 29 matchsticks​ wide, how many matchsticks are​ used?

678

How many integers between 100 & 400 contain the digit 2?

138

Determine the number of triangles​ (of any​ size) in the figure.

14

How many of the numbers from 10 through 88 have the sum of their digits equal to a perfect​ square?

15 90=16

Evaluate the expression. 7P3

210

Evaluate 15!/12!

2730

A panel containing 5 on-off switches in a row is to be set. Assuming no restrictions on individual​ switches, use the fundamental counting principle to find the total number of possible panel settings.

32

Counting numbers are to be formed using only the digits 2, 6​, and 7 Determine the number of different possibilities for the type of number described below. ​Four-digit numbers with one pair of adjacent 2s and no other repeated digits​ (Hint: You may want to split the task of designing such a number into three​ parts, such as​ (1) position the pair of 2​s, ​(2) position the 6​, and​ (3) position the 7​.)

3x2x1=6

A line segment joins the points ​(8,14​) and ​(62​,227​) in the Cartesian plane. Including its​ endpoints, how many lattice points does this line segment​ contain? (A lattice point is a point with integer​ coordinates.)

4

Evaluate. 17! / 14!

4080

Evaluate the expression without using a calculator. 32! / 30! * 2!

4961

A line segment joins the points ​(7​,14​) and ​(71​,282​) in the Cartesian plane. Including its​ endpoints, how many lattice points does this line segment​ contain? (A lattice point is a point with integer​ coordinates.)

5

Pamela​ DeMar's computer printer allows for optional settings with a panel of 3 ​on-off switches in a row. How many different settings can she select if no 2 adjacent switches can both be​ on?

5

Evaluate the expression without using a calculator 43! / 41! * 2!

903

Evaluate the expression without using a calculator 45! / 43! * 2!

990

Ann​'s collection of eight albums includes one classical album. Ann will choose four of her albums to play on a road trip.​ (Assume order is not​ important.) ​a) How many different sets of four albums could she​ choose? ​b) How many of these sets would not include the classical ​album? ​c) How many of them would include the classical ​album?

A. 70 B. 35 C. 35

A club N with 4 members is shown below: {Alfred, Blake, Carrie, Douglas} Assuming all members of the club are eligible, but no one can hold more than one office, list and count the different ways the club could elect both a president and a treasurer

AB,AC,AD,BA,BC,BD,CA,CB,CD,DA,DB,DC 12

Assuming all members of the club are​ eligible, but that no one can hold more than one​ office, list and count the different ways the club could elect a president and a treasurer if the two officers must be the same gender. N = {Alvin, Ben, Carrie, Dennis, Eileen}

AB,AD,BA,BD,CE,DA,DB,EC 8

Assuming all members of the club are​ eligible, but that no one can hold more than one​ office, list and count the different ways the club could elect a president and a treasurer if the two officers must not be the same gender. N = {Aaron, Bob, Carla, Dennis, Eileen}

AC, AE, BC, BE, CA, CB, CD, DC, DE, EA, EB, ED 12

Assuming all members are​ eligible, but no one can hold more than one​ office, list and count the different ways the club could elect a​ president, a​ secretary, and a treasurer if the president must be a man and the other two must be women. ​(Carol & Erica are​ women, and the others are​ men.) N= {Aaron, Ben, Carol, Dennis, Erica} ​or, in abbreviated​ form, N= {A, B, C, D, E}

ACE, AEC,​ BCE, BEC,​ DCE, DEC 6

Construct a tree diagram showing all possible results when three fair coins are tossed. Then list the ways of getting the following result. fewer than two heads

C TTT,HTT,THT,TTH

Determine whether the object is a permutation or a combination. a​ 10-digit telephone number​ (including area​ code)

Choose the correct answer below: This is neither a permutation nor a combination because repetition is allowed.

Refer to the table below. Of the 36 possible​ outcomes, determine the number for which the sum​ (for both​ dice) is 3.

One can roll a sum of 3 in __2__ way(s).

For​ $3.98 you can get a​ salad, main​ course, and dessert at the cafeteria. If you have a choice of 4 different​ salads, 7 different main​ courses, and 5 different​ desserts, then how many different meals can you get for​ $3.98?

For the event of choosing a​ salad, the number of possible outcomes is 4. For the event of choosing a main​ course, the number of possible outcomes is 7. For the event of choosing a​ dessert, the number of possible outcomes is 5. Applying the fundamental counting principle you have 4 x 7 x 5=140.

Refer to the table below. Of the 36 possible​ outcomes, determine the number for which the sum​ (for both​ dice) is 12.

One can roll a sum of 12in _1__​way(s).

On the 16 numbers in the product table, list the ones that belong in the category: 2, 3, 7, 9

Prime numbers are: 23,29,37,73,79,97

How many ways can a teacher give 3 different prizes to 3 of her 25 students?

She an award the prizes __13,800__ ways.

How many ways can a teacher give 6 different prizes to six of her 21 students?

She can award the prizes in __39,070,080_ ways.

How many ways can a teacher give 5 different prizes to 5 of her 23 students?

She can award the prizes in __4,037,880___ ways.

​Jessica's class schedule for next semester must consist of exactly one class from each of the four categories shown in the table. Category Number of Choices: Economics 6 Mathematics 3 Education 4 Sociology 4 All sections for the 3 most popular classes in Economics are full. The rest of the courses are available. Determine the number of different sets of classes Jessica can take.

The basic task is to design a schedule with a class from each category. There are four components to this task. The number of available Economics courses must be changed since 3 of the courses are full. The number of available Economics courses is 6-3=3 Now use the fundamental counting principle to multiply the number of options in each category. 3 x 3 x 4 x 4 =144 Jessica has 144 different sets of classes to choose from.

Find the number of combinations​ (subsets) of 8 things taken 3 at a time.

The number is __5____ combinations

A customer ordered 17 zingers. Zingers are placed in packages of​ 4, 3, or 1. In how many different ways can this order be​ filled?

The number of possible different ways is 17.

Determine the total number of proper subsets of the set of letters from the English alphabet {a, b, c, ..., l}.

The number of proper subsets is __4095_____.

Jason wants to dine at 5 different restaurants during a summer getaway. If 2 of 8 available restaurants serve​ seafood, find the number of ways that at least 1 of the selected restaurants will serve seafood given the condition that the order of selection is important.

The number of ways that at least one of the selected restaurants will serve seafood is __6000__

Jason wants to dine at 3 different restaurants during a summer getaway. If 2 of 6 available restaurants serve​ seafood, find the number of ways that at least 1 of the selected restaurants will serve seafood given the condition that the order of selection is important.

The number of ways that at least one of the selected restaurants will serve seafood is __96___.

Jason wants to dine at 5 different restaurants during a summer getaway. If 2 of 10 available restaurants serve​ seafood, find the number of ways that at least 1 of the selected restaurants will serve seafood given the condition that the order of selection is important.

The number of ways that at least one of the selected restaurants will serve seafood is ____23250______.

Evaluate the expression. 6P3

The solution is 120

Evaluate the expression 9P2

The solution is 72

Evaluate 14! / 11!

The solution is _2184__ .

determine the number of squares (of any size) in the figure

The total number of squares is 30

Determine the number of triangles​ (of any​ size) in the figure.

The total number of triangles _20_

Determine the number of triangles​ (of any​ size) in the figure.

The total number of triangles is __16______.

Determine the number of triangles​ (of any​ size) in the figure.

The total number of triangles is ___12_____.

Of the 16 numbers in the product table, list the ones that belong in the category: Prime Numbers: 2,3,7,9

There are 18 outcome where the sum is odd

Find the number of distinguishable arrangements of the letters of the word. QUINTILLION

There are _1,663,200___ distinguishable arrangements

A baseball team has 6 ​pitchers, who only​ pitch, and 16 other​ players, all of whom can play any position other than pitcher. For​ Saturday's game, the coach has not yet determined which 9 players to use nor what the batting order will​ be, except that the pitcher will bat last. How many different batting orders may​ occur?

There are _3,113,510,400_ different batting orders

How many 2-digit counting numbers are not multiples of 5?

There are _72____ 2-digit counting numbers which are not multiples of 5.

How many 2-digit counting numbers are not multiples of 10?

There are _81_ 2-digit counting numbers which are not multiples of 10.

Find the number of distinguishable arrangements of the letters of the word. MILLIARD

There are __10,080_ distinguishable arrangements.

A baseball team has 8 ​pitchers, who only​ pitch, and 9 other​ players, all of whom can play any position other than pitcher. For​ Saturday's game, the coach has not yet determined which 9 players to use nor what the batting order will​ be, except that the pitcher will bat last. How many different batting orders may​ occur?

There are __2,903,040____ different batting orders

Find the number of distinguishable arrangements of the letters of the word. TREDECILLION

There are __59,875,200___ distinguishable arrangements

A baseball team has 5 ​pitchers, who only​ pitch, and 14 other​ players, all of whom can play any position other than pitcher. For​ Saturday's game, the coach has not yet determined which 9 players to use nor what the batting order will​ be, except that the pitcher will bat last. How many different batting orders may​ occur?

There are __605,404,800__ different batting orders

A​ multiple-choice test consist of 6 questions with each question having 3 possible answers.

To find the number of ways to mark the​ answers, use the Fundamental Counting Principle​ (or Multiplication​ Principle). Notice you cannot use permutations since repetitions are possible. Determine the number of possible outcomes for each event and multiply these together. For the event of choosing an answer for the first​ question, the number of possible outcomes is 3. For the event of choosing an answer for the second​ question, the number of possible outcomes is 3. Continuing in this​ manner, you can see that for each of the 6 events of choosing an​ answer, there are 3 possible outcomes. The number of ways to mark the answers is 3 x 3 x 3 x 3 x 3 x 3 ​= 729.

Five men and five women have just six tickets in one row to the theater. In how many ways can they sit if the men and women are to alternate with either a man or a woman in the first​ seat?

a.) The first seat can be anyone. There are 10 choices of people for the first seat. ​b.) The second seat must be someone from the opposite sex of the person in the first seat. There are 5 choices for the second seat. ​c.) The third seat must be someone of the same sex as the first seat. There is one person sitting in the first seat already. There are 4 choices for the third seat. ​d.) The fourth seat must be the same sex as the second seat. There is one person sitting in the second seat already. There are 4 choices for the fourth seat. ​e.) The fifth seat must be someone of the same sex as the first and third seats. Two people of this sex are already seated. There are 3 choices for the fifth seat. ​f.) The sixth seat must be someone of the same sex as the second and fourth seats. Two people of this sex are already seated. There are 3 choices for the sixth seat. ​g.) Now find the product 10 x 5 x 4 x 4 x 3 x 3. 10 x 5 x 4 x 4 x 3 x 3 = 7,200 ​Therefore, five men and five women can sit down in 6 seats in 7,200 ways alternating sexes with either a man or a woman in the 1st seat.

Construct a tree diagram showing all possible results when 3 fair coins are tossed. Then list the ways of getting the following result. @ least 2 tails

construct a tree diagram. Choose the correct diagram below. A Select the correct choice below that lists the appropriate branches. TTH,THT, HTT, TTT

Refer to the table below. Of the 36 possible​ outcomes, determine the number for which the sum​ (for both​ dice) is 5.

one can roll a sum of 5 in "4" ways

Pamela's computer printer allows for optional settings with a panel of 4 ​on-off switches in a row. How many different settings can she select if there are no restraints

she can select 16 different settings

​Pamela's computer printer allows for optional settings with a panel of 3 on-off switches in a row. How many different settings can she select if there are no restrictions on the switches​?

she can select 32 different settings

Pamela's computer printer allows for optional settings with a panel of 6 ​on-off switches in a row. How many different settings can she select if at least one switch must be on​?

she can select 63 different settings

Pamela's computer printer allows for optional settings with a panel of 4 ​on-off switches in a row. How many different settings can she select if at least one switch must be on​?

she can select __15__ different settings

Determine the total number of proper subsets of the set of letters from the English alphabet {a, b, c, ..., h}.

the number of proper subsets is __255___.


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