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Chapter 6: Problem 35
A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles. How many sets of four marbles include one of each color other than lavender?
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If a die is rolled 30 times, there are \(6^{30}\) different sequences possible.Ask how many of these sequences satisfy certain conditions. What fraction of these sequences have exactly 15 even numbers?
Exercises are based on the following table, which shows the performance of a selection of 100 stocks afier one year. (Take \(S\) to be the set of all stocks represented in the table.) Calculate \(\frac{n(D \cap I)}{n(D)} .\) What does the answer represent?
Explain why the coefficient of \(a^{2} b^{4}\) in \((a+b)^{6}\) is \(C(6,2)\) (this is a consequence of the binomial theorem).
Which of the following represent combinations? (A) A portfolio of five stocks chosen from the S\&P Top Ten (B) A group of 5 tenors for a choir chosen from 12 singers (C) A new company CEO and a new CFO chosen from five (D) The New York Times Top Ten Bestseller list
Use Venn diagrams to illustrate the following identities for subsets \(A, B\), and \(\operatorname{Cof} S .\) $$ (A \cap B)^{\prime}=A^{\prime} \cup B^{\prime} \quad \text { De Morgan's Law } $$
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