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Chapter 6: Problem 24
How many three-letter sequences are possible that use the letters \(\mathrm{b}, \mathrm{o}, \mathrm{g}, \mathrm{e}, \mathrm{y}\) at most once each?
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Entertainment In a survey of 100 Enormous State University students, 21 enjoyed classical music, 22 enjoyed rock music, and 27 enjoyed house music. Five of the students enjoyed both classical and rock. How many of those that enjoyed rock did not enjoy classical music?
Use Venn diagrams to illustrate the following identities for subsets \(A, B\), and \(\operatorname{Cof} S .\) $$ (A \cup B)^{\prime}=A^{\prime} \cap B^{\prime} \quad \text { De Morgan's Law } $$
A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles. How many sets of five marbles include at most one of the red ones?
Home Sales Exercises are based on the following table, which shows the number of sales of existing homes, in millions, in the different regions of the United States during \(2006-2008 .\) Take \(S\) to be the set of all home sales represented in the table and label the sets representing the home sales in each row and column as shown (so that, for example, \(N\) is the set of all sales of existing homes in the Northeast during \(2006-2008\) ) Use symbols to describe each set, and compute its cardinality. The set of sales of existing homes in the South and West in years other than 2006
When is \(n(A \cap B)=n(A) ?\)
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