Exam 6: Sets and Counting

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

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

In recent years, the state of California issued license plates using a combination of two letters of the alphabet followed by two digits, followed by another three letters of the alphabet. How many different license plates can be issued using this configuration?

Find the smallest possible set (that is, the set with the least number of elements) that contains the given sets as subsets. ​

Let A, B, and C be subsets of a universal set U and suppose , , , , , , , and . Compute: ​ __________ ​ __________

An opinion poll is to be conducted among cable TV viewers. Four multiple-choice questions, each with three possible answers, will be asked. In how many different ways can a viewer complete the poll if exactly one response is given to each question? ​ __________ different ways

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

Write the following set in builder notation form ​

In a survey of 116 consumers conducted in a shopping mall, 79 consumers indicated that they buy brand A of a certain product, 64 buy brand B, and 43 buy both brands. How many consumers participating in the survey buy at least one of these brands? How many consumers participating in the survey buy exactly one of these brands? How many consumers participating in the survey buy only brand A? How many consumers participating in the survey buy none of these brands? ​ __________ consumers bought at least one of these brands ​ __________ consumers bought exactly one of these brands ​ __________ consumers bought only brand A ​ __________ consumers bought none of these brands

In how many different ways can a panel of 12 jurors and 2 alternate jurors be chosen from a group of 27 prospective jurors? ​

In a survey of 200 employees of a company regarding their 401K investments, the following data were obtained: ​ 142 had investments in stock funds. ​ 89 had investments in bond funds. ​ 62 had investments in money market funds. ​ 47 had investments in stock funds and bond funds. ​ 38 had investments in stock funds and money market funds. ​ 36 had investments in bond funds and money market funds. ​ 5 had investments in some other vehicle. ​ How many of the employees surveyed had investments in all three types of funds? How many of the employees had investments in stock funds only? ​ __________ employees have investments in all three types of funds ​ __________ employees have investments in stock funds only

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

UBS Television Company is considering bids submitted by seven different firms for three different contracts. In how many ways can the contracts be awarded among these firms if no firm is to receive more than two contracts? ​ __________ ways

Let and . Compute n(A). ​

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Let U denote the set of all senators in Congress. Let ​ ​ Write the set that represents the following statement: ​ The set of all Republicans who are female and are lawyers. ​

Computers manufactured by a certain company have a serial number consisting of a letter of the alphabet followed by a five-digit number. If all the serial numbers of this type have been used, how many sets have already been manufactured? ​

A computer dating service uses the results of its compatibility survey for arranging dates. The survey consists of 30 questions, each having five possible answers. How many different responses are possible if every question is answered? ​

Let A, B, and C be subsets of a universal set U and suppose , , , , , , , and . Compute: ​ __________ ​ __________

In recent years, the state of California issued license plates using a combination of one letter of the alphabet followed by two digits, followed by another three letters of the alphabet. How many different license plates can be issued using this configuration? ​ __________ different license plates