# 7.6: Chapter 7 Review

- Page ID
- 147306

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### Sets and Counting (7.1)

- Suppose of the 4,000 freshmen at a college everyone is enrolled in a mathematics or an English class during a given quarter. If 2,000 are enrolled in a mathematics class, and 3,000 in an English class, how many are enrolled in both a mathematics class and an English class?
- In a survey of 250 people, it was found that 125 had read Time magazine, 175 had read Newsweek, 100 had read U. S. News, 75 had read Time and Newsweek, 60 had read Newsweek and U. S. News, 55 had read Time and U. S. News, and 25 had read all three.
- How many had read Time but not the other two?
- How many had read Time or Newsweek but not the U. S. News And World Report?
- How many had read none of these three magazines?

### Tree Diagrams and the Multiplication Axiom (7.2)

- At a manufacturing plant, a product goes through assembly, testing, and packing. If a plant has three assembly stations, two testing stations, and two packing stations, in how many different ways can a product achieve its completion?
- Six people are to line up for a photograph. How many different lineups are possible if three of them insist on standing next to each other?
- How many four-letter word sequences can be made from the letters of the word OXYGEN?
- In how many different ways can a 20-question multiple choice test be designed so that its answers contain 2 A's, 4 B's, 9 C's, 3 D's, and 2 E's?

### Permutations and Combinations (7.3 & 7.4)

- How many three digit even numbers can be formed from the digits 1, 2, 3, 4, 5 if no repetitions are allowed?
- Compute:
- \(9\mathrm{C}4\)
- \(8\mathrm{P}3\)
- \(\frac{10 !}{4 !(10-4) !}\)

- From a group of 6 people, 3 are assigned to cleaning, 2 to hauling and one to garbage collecting. How many different ways can this be done?
- In how many ways can 3 books be selected from 4 English and 2 History books if at least one English book must be chosen?
- A club consists of six men and nine women. In how many ways can a president, a vice president and a treasurer be chosen if the two of the officers must be women?
- Of its 12 sales people, a company wants to assign 4 to its Western territory, 5 to its Northern territory, and 3 to its Southern territory. How many ways can this be done?
- How many five-card poker hands consisting of the following distribution are there?
- A flush(all five cards of a single suit)
- Three of a kind(e.g. three aces and two other cards)
- Two pairs(e.g. two aces, two kings and one other card)
- A straight(all five cards in a sequence)

- Company stocks on an exchange are given symbols consisting of three letters. How many different three-letter symbols are possible?
- A United Nations delegation consists of 6 Americans, 5 Russians, and 4 Chinese. Answer the following questions.
- How many committees of five people are there?
- How many committees of three people consisting of at least one American are there?
- How many committees of four people having no Russians are there?
- How many committees of three people have more Americans than Russians?
- How many committees of three people do not have all three Americans?

- If a coin is flipped five times, in how many different ways can it show up three heads?

### Binomial Theorem (7.5)

- Find the fourth term of the expansion \((2x - 3y)^8\).
- Find the coefficient of the \(a^5 b^4\) term in the expansion of \((a – 2b)^9\).