Exam 6: Sets and Counting

Four items from three different departments of Metro Department Store will be featured in a one-page newspaper advertisement as shown in the following diagram. ​ ​ If items from the same department must be in the same row, how many arrangements are possible? ​

How many four-letter code words can be constructed from the first ten letters of the Greek alphabet if no repetitions allowed? ​

In a survey conducted by a union, members were asked to rate the importance of the following issues: (1) job security, (2) increased fringe benefits, and (3) improved working conditions. Three different responses were allowed for each issue. Among completed surveys, how many different responses to this survey were possible? ​ __________ different responses

In how many ways can a member of a hiring committee select 6 of 17 job applicants for further consideration? ​

The number of three-digit numbers that can be formed from the digits 1, 2, 3, and 4 if the number must be even is 19.

In a state lottery there are 12 finalists eligible for the Big Money Draw. In how many ways can the first, second, and third prizes be awarded if no ticket holder may win more than one prize? ​

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

Evaluate the expression. ​ ​

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

In how many ways can a -letter security password be formed from letters of the alphabet if no letter is repeated? ​

Let U denotes the set of all students who applied for admission to fresman class at faber college for the upcoming academic year, and let Determine which of the following statements are true. i) ii) iii)

If , , and , what is ? ​

In a survey of 380 households regarding the ownership of VCRs and DVD players, the following data was obtained: ​ 350 households own one or more VCRs. ​ 180 households own one or more VCRs and one or more DVD players. ​ 13 households do not own a VCR or a DVD player. ​ How many households only own one or more DVD players? ​

In a survey conducted by a union, members were asked to rate the importance of the following issues: (1) job security, (2) increased fringe benefits, and (3) improved working conditions. Three different responses were allowed for each issue. Among completed surveys, how many different responses to this survey were possible? ​

Use venn daigram to illustrate the statement. ​

The 120 consumers were asked about their buying preferences concerning another product that is sold in the market under three labels. The results were ​ 12 buy only those sold under label A. ​ 24 buy only those sold under label B. ​ 27 buy only those sold under label C. ​ 14 buy only those sold under labels A and B. ​ 9 buy only those sold under labels A and C. ​ 11 buy only those sold under labels B and C. ​ 7 buy the product sold under all three labels. ​ How many of the consumers surveyed buy the product sold under none of these labels? ​

How many seven-digit telephone numbers are possible if the first digit must be nonzero? ​ __________ ​ 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 number of the type described in part (a)? ​ __________

In a poll conducted among active investors, it was found that use discount brokers, use full-service brokers, and use both discount and full-service brokers. How many investors use only discount brokers? ​

Let . ​ ​

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