Exam 6: Sets and Counting

A survey of 100 college students who frequent the reading lounge of a university revealed the following results: ​ 47 read Time. ​ 36 read Newsweek. ​ 31 read U.S. News & World Report. ​ 19 read Time and Newsweek. ​ 16 read Time and U.S. News & World Report. ​ 12 read Newsweek and U.S. News & World Report. ​ 6 read all three magazines. ​ How many of the students surveyed read none of these magazines? ​ __________ students

Let . Which of the following sets are equal to A? ​

List the elements of the given set in roster notation. ​ ​

Of 55 employees of a store located in downtown Boston, 18 people take the subway to work, 15 take the bus, and 6 take both the subway and the bus. ​ How many employees take the subway or the bus to work? __________ ​ How many employees take only the bus to work? __________ ​ How many employees take either the bus or the subway to work? __________ ​ How many employees get to work by some other means? __________

How many eight-letter permutations can be formed from the first letters of the alphabet? ​

Let U denote the set of all employees at Universal Life Insurance Company. Let ​ ​ Match each description below with the letter of the corresponding set. ​ a. b. c. d. -drinks coffee but does not drink tea

In how many ways can six students be seated in a row of six seats? ​

In how many ways can a member of a hiring committee select 7 of 19 job applicants for further consideration? ​ __________ ways

A student planning her curriculum for the upcoming year must select one of six Business courses, one of seven Mathematics courses, two of three elective courses, and either one of four History courses or one of seven Social Science courses. How many different curricula are available for her consideration? ​

In how many ways can an investor select five mutual funds for his investment portfolio from a recommended list of eight mutual funds? ​ __________ ways

How many international direct-dialing numbers are possible if each number consists of a four-digit area code (the first digit of which must be nonzero) and a five-digit telephone numbers (the first digit must be nonzero)? ​

Let ​ ​ Verify by direct computation the equation. ​ ​

Let . If and , find ​ __________ ​ __________ ​ __________ ​ __________

In a survey of 122 consumers conducted in a shopping mall, 83 consumers indicated that they buy brand A of a certain product, 69 buy brand B, and 46 buy both brands. How many consumers participating in the survey buy at least one of these brands? ​

In a survey of 300 individual investors regarding subscriptions to the New York Times (NYT), Wall Street Journal (WSJ), and USA Today (UST), the following data were obtained. ​ 123 subscribe to the NYT. ​ 149 subscribe to the WSJ. ​ 64 subscribe to the UST. ​ 36 subscribe to the NYT and WSJ. ​ 26 subscribe to the WSJ and UST. ​ 21 subscribe to the NYT and UST. ​ 34 do not subscribe to any of these newspapers. ​ How many of the individual investors surveyed subscribe to all three newspapers? ​ __________ ​ How many subscribe to only one of these newspapers? ​ __________

If , , and , what is ? ​ __________