Question 1

A telephone number consists of a sequence of seven digits not starting with a 0 or a 1. How many phone numbers begin with either 764, 768, or 788

Accepted Answer

The answer of A telephone number consists of a sequence...

Question 2

The World Almanac features a "perpetual calendar", a collection of 14 possible calendars. Why does this suffice to be sure there is a calendar for every conceivable year

Accepted Answer

The answer of The World Almanac features a "perpetual calendar",...

Question 3

A test requires that you answer either Part A or Part B. Part A consists of 21 true/false questions and part B consists of 9 multiple choice questions with one correct answer out of 5. How many different completed answer sheets are possible

Accepted Answer

The answer of A test requires that you answer either...

Question 4

Professor Tough's final examination has 13 true-false questions followed by 5 multiple-choice questions. In each of the multiple choice questions you must select the correct answer from a list of 5. How many answer sheets are possible 
 
__________ sheets

Accepted Answer

The answer of Professor Tough's final examination has 13 true-false...

Question 5

While selecting candy for students in his class, Professor Murphy must choose between gummy candy and licorice nibs. Gummy candy packets come in 4 sizes, and packets of licorice nibs come in 2 sizes.
If he chooses gummy candy, he must select gummy lions, gummy bears, gummy worms or gummy dinos. If he chooses licorice nibs, he must choose between red and black. How many choices does he have

Accepted Answer

The answer of While selecting candy for students in his...

Question 6

Use the given information to complete the solution to the partially solved Venn diagram.   $$n ( A ) = 24$$ , $n ( B ) = 19$ , $n ( C ) = 30$ , $n ( A \cap C ) = 6$ , and $n ( S ) = 51$

Accepted Answer

The answer of Use the given information to complete the...

Question 7

A test requires that you answer first Part A and then either Part B or Part C. Part A consists of 6 true/false questions, Part B consists of 9 multiple choice questions with one correct answer out of 5, and Part C requires you to match 8 questions with 8 different answers. (Each question matches exactly one correct answer.) How many different completed answer sheets are possible  ?
__________ sheets

Accepted Answer

The answer of A test requires that you answer first...

Question 8

Find how many outcomes are possible for the decision algorithms. $\begin{array}{ll}
{\text { Step } 1} & \text { Step } 2 \
\text { Alternative 1:1 outcome } & \text { Alternative } 1: 2 \text { outcomes } \
\text { Alternative } 2: 1 \text { outcome } & \text { Alternative } 2: 2 \text { outcomes } \
\text { Alternative } 3: 1 \text { outcome } &
\end{array}$ ​​
__________ outcomes

Accepted Answer

The answer of Find how many outcomes are possible for...

Question 9

Find how many outcomes are possible for the decision algorithms. $\begin{array}{cl}
{\text { Step 1 }} &{\text { Step 2 }} \
\text { Alternative 1:1 outcome } & \text { Alternative 1:2 outcomes } \
\text { Alternative 2: } 1 \text { outcome } & \text { Alternative } 2: 2 \text { outcomes } \
& \text { Alternative } 3: 2 \text { outcomes }
\end{array}$ ​
__________ outcomes

Accepted Answer

The answer of Find how many outcomes are possible for...

Question 10

Professor Oger must choose between an extra writing assignment and an extra reading assignment for the upcoming spring break. For the writing assignment, there are 4 essay topics to choose from and three different mandatory lengths (30 pages, 35 pages, or 40 pages). The reading topic would consist of one scholarly biography combined with one volume of essays. There are 4 biographies and four volumes of essays to choose from. How many choices does she have

Accepted Answer

The answer of Professor Oger must choose between an extra...

Question 11

A surgical procedure requires four steps. The first step can result in 6 possible outcomes, the second in 4 possible outcomes, and the remaining two can each result in 3 possible outcomes. What is the total number of outcomes possible

Accepted Answer

The answer of A surgical procedure requires four steps. The...

Question 12

A Social Security number is a sequence of nine digits. How many Social Security numbers are possible that have the same first 6 digits

Accepted Answer

The answer of A Social Security number is a sequence...

Question 13

Find how many outcomes are possible for the decision algorithms. $\begin{array}{lc}
\text { Alternative 1 } & \text { Alternative 2 } \
\text { Step 1: four outcomes } & \text { Step 1: three outcomes } \
\text { Step 2: four outcomes } & \text { Step 2: five outcomes } \
& \text { Step 3: three outcomes }
\end{array}$

Accepted Answer

The answer of Find how many outcomes are possible for...

Question 14

In an eight-cylinder engine, the even-numbered cylinders are on the left and the odd-numbered cylinders are on the right. A good firing order is a sequence of the numbers 1 through 8 in which right and left sides alternate.
 
a. How many possible good firing sequences are there  ?
__________ sequences
 
b. How many good firing sequences are there that start with a cylinder on the left  ?
__________ sequences

Accepted Answer

The answer of In an eight-cylinder engine, the even-numbered cylinders...

Question 15

Of the 5,700 students at medium Suburban College, 50 play collegiate soccer, 60 play collegiate lacrosse, and 80 play collegiate football. Only 4 play both collegiate soccer and lacrosse, 6 play collegiate soccer and football, and 15 play collegiate lacrosse and football. No students play all three sports. ​
Complete the following sentence: ______% of the college soccer players also play one of the other two sports at the collegiate level.
​

Accepted Answer

The answer of Of the 5,700 students at medium Suburban...

Question 16

A computer "byte" consists of 8 "bits", each bit being either a 0 or a 1. If characters are represented using a code that uses 4 bytes for each character, how many characters can be represented  ?
__________ characters

Accepted Answer

The answer of A computer "byte" consists of 8 "bits",...

Question 17

In December 2001 a search using the Web search engine Google^TM for "Costenoble" yielded 10,000 Web sites containing that word. A search for "Waner" yielded 67,000 sites. A search for sites containing both words yielded 4,393 sites. How many Web sites contained either "Costenoble" or "Waner" or both ?

Accepted Answer

To find the total number of websites containing either "Costenoble" or "Waner" or both, we use the principle of inclusion-exclusion. We add the total number of sites for each word and subtract the number of sites that contain both words to avoid double-counting. So, $10,000 + 67,000 - 4,393 = 72,607$.

Question 18

How many possible calendars are there that have February 15 falling on a Monday, or Tuesday  ?
__________ calendars

Accepted Answer

The answer of How many possible calendars are there that...

Question 19

Some written languages, such as Chinese and Japanese, use tens of thousands of different characters. If a language uses 16,384 characters, a computer code for this language would have to use how many bits (1 or 0) per character

Accepted Answer

The answer of Some written languages, such as Chinese and...

Question 20

Dripping wet after your shower, you have clean forgotten the combination of your lock. It is one of those "standard" combination locks, which uses a three-number combination with each number in the range 0 through 39. All you remember is that the second number is either 27 or 37, while the third number ends in a 4. In desperation, you decide to go through all possible combinations using the information you remember. Assuming that it takes about 10 seconds to try each combination, what is the longest possible time you may have to stand dripping in front of your locker  ?
Assume that 4 does not end with a 4 .
 
__________ minutes

Accepted Answer

The answer of Dripping wet after your shower, you have...

Quiz 7: Sets and Counting

A telephone number consists of a sequence of seven digits not starting with a 0 or a 1. How many phone numbers begin with either 764, 768, or 788

The World Almanac features a "perpetual calendar", a collection of 14 possible calendars. Why does this suffice to be sure there is a calendar for every conceivable year

A test requires that you answer either Part A or Part B. Part A consists of 21 true/false questions and part B consists of 9 multiple choice questions with one correct answer out of 5. How many different completed answer sheets are possible

Professor Tough's final examination has 13 true-false questions followed by 5 multiple-choice questions. In each of the multiple choice questions you must select the correct answer from a list of 5. How many answer sheets are possible __________ sheets

Use the given information to complete the solution to the partially solved Venn diagram. n(A) =24n ( A ) = 24n(A) =24 , n(B) =19n ( B ) = 19n(B) =19 , n(C) =30n ( C ) = 30n(C) =30 , n(A∩C) =6n ( A \cap C ) = 6n(A∩C) =6 , and n(S) =51n ( S ) = 51n(S) =51

A surgical procedure requires four steps. The first step can result in 6 possible outcomes, the second in 4 possible outcomes, and the remaining two can each result in 3 possible outcomes. What is the total number of outcomes possible

A Social Security number is a sequence of nine digits. How many Social Security numbers are possible that have the same first 6 digits

A computer "byte" consists of 8 "bits", each bit being either a 0 or a 1. If characters are represented using a code that uses 4 bytes for each character, how many characters can be represented ? __________ characters

How many possible calendars are there that have February 15 falling on a Monday, or Tuesday ? __________ calendars

Some written languages, such as Chinese and Japanese, use tens of thousands of different characters. If a language uses 16,384 characters, a computer code for this language would have to use how many bits (1 or 0) per character