CH 10 review quiz
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 2s, (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___.
