Exam 6: Sets and Counting

A female executive selecting her wardrobe purchased three blazers, five blouses, and five skirts in coordinating colors. How many ensembles consisting of a blazer, a blouse, and a skirt can she create from this collection? ​

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

Of 120 clock radios sold recently in a department store, 110 had FM circuitry, and 100 had AM circuitry. ​ How many radios had both FM and AM circuitry? __________ ​ How many could receive FM transmission only? __________ ​ How many could receive AM transmission only? __________

Refer to the accompanying figure and find the points that belong the set . ​ ​

How many different batting orders can be formed for a nine-member baseball team? ​ __________ batting orders

Evaluate the expression. ​

Evaluate the expression. ​ ​

Of 100 clock radios sold recently in a department store, 60 had FM circuitry, and 80 had AM circuitry. How many could receive FM transmission only? ​

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

A warranty identification number for a certain product consists of a letter of the alphabet followed by a four-digit number. How many possible identification numbers are there if the first digit of the four-digit number must be nonzero? ​

UBS Television Company is considering bids submitted by twelve 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? ​

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

A survey of the opinions of leading Economists in a certain country showed that, because oil prices were expected to drop in that country over the next 12 months, had lowered their estimate of the consumer inflation rate, had raised their estimate of the gross national product (GNP) growth rate. had lowered their estimate of the consumer inflation rate but had not raised their estimate of the GNP growth rate. How many Economists had raised their estimate of GNP growth rate and lowered their estimate of the consumer inflation rate for that period? ​

Refer to the accompanying figure and find the points that belong the set . ​

Let Verify by direct computation each equation. a. b.

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

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

If , , , , , , and find . ​

Over the years one state has used different combinations of letters of the alphabet and digits on its automobile license plates. At one time, license plates were issued that consisted of three letters followed by three digits. How many different license plates can be issued under this arrangement? ​ __________ different license plates

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 tea but does not drink coffee