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Chapter 6: Problem 23
How many three-letter sequences are possible that use the letters \(\mathrm{q}, \mathrm{u}, \mathrm{a}, \mathrm{k}, \mathrm{e}, \mathrm{s}\) at most once each?
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Spending in most categories of health care in the United States increased dramatically in the last 30 years of the \(1900 \mathrm{~s} .{ }^{1}\) You are given data showing total spending on prescription drugs, nursing homes, hospital care, and professional services for each of the last three decades of the \(1900 \mathrm{~s}\). How would you represent these data in a spreadsheet? The cells in your spreadsheet represent elements of which set?
Minimalist Art You are exhibiting your collection of minimalist paintings. Art critics have raved about your paintings, each of which consists of 10 vertical colored lines set against a white background. You have used the following rule to produce your paintings: Every second line, starting with the first, is to be either blue or grey, while the remaining five lines are to be either all light blue, all red, or all purple. Your collection is complete: Every possible combination that satisfies the rules occurs. How many paintings are you exhibiting?
Based on the following list oftop \(D V D\) rentals (based on revenue) for the weekend ending January 4, 2009:$$\begin{array}{|l|c|}\hline \text { Name } & \text { Rental Index } \\\\\hline \text { EagleEye } & 100.00 \\\\\hline \text { Burn After Reading } & 74.62 \\\\\hline \text { Mamma Mia! } &63.30\\\\\hline \text { The Dark Knight } & 62.43 \\\\\hline \text { Death Race } & 61.50 \\\\\hline\begin{array}{l}\text { The Mummy: Tomb of the } \\\\\text { Dragon Emperor }\end{array} & 60.72 \\\\\hline \text { Traitor } & 52.57 \\\\\hline \text { Wanted } & 49.22 \\\\\hline \text { Step Brothers } & 46.81 \\\\\hline \text { Horton Hears a Who! } & 43.91 \\\\\hline\end{array}$$ Rather than study for math, you and your buddies decide to get together for a marathon movie-watching popcornguzzling event on Saturday night. You decide to watch four movies selected at random from the above list. a. How many sets of four movies are possible? b. Your best friends, the Lara twins, refuse to see Horton Hears a Who! on the grounds that it is "for girlie men" and also insist that at least one of Death Race or Eagle Eye be among the movies selected. How many of the possible groups of four will satisfy the twins? c. Comparing the answers in parts (a) and (b), would you say the Lara twins are more likely than not to be satisfied with your random selection?
Use Venn diagrams to illustrate the following identities for subsets \(A, B\), and \(\operatorname{Cof} S .\) $$ A \cup(B \cap C)=(A \cup B) \cap(A \cup C) \quad \text { Distributive Law } $$
A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles. How many possible sets of three marbles are there?
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