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Chapter 6: Problem 33
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 none of the red ones?
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License Plates \(^{12}\) License plates in Montana have a sequence consisting of: (1) a digit from 1 to \(9,(2)\) a letter, \((3)\) a dot, (4) a letter, and (5) a four-digit number. a. How many different license plates are possible? b. How many different license plates are available for citizens if numbers that end with 0 are reserved for official state vehicles?
Day traders typically buy and sell stocks (or other investment instruments) during the trading day and sell all investments by the end of the day. Exercises 57 and 58 are based on the following table, which shows the closing prices on January 9, 2009, of 12 stocks selected by your broker, Prudence Swift, as well as the change that day.$$\begin{array}{|l|c|c|}\hline \text { Tech Stocks } & \text { Close } & \text { Change } \\\\\hline \text { AAPL (Apple) } & \$ 90.58 & -2.12 \\\\\hline \text { MSFT (Microsoft) } & \$ 19.52 & -0.60 \\\\\hline \text { NOK (Nokia) } & \$ 15.21 & -0.16 \\\\\hline \text { NT (Nortel) } & \$ 0.39 & 0.10 \\\\\hline \text { RIMM (Research in Motion) } & \$ 47.99 & 1.49 \\\\\hline \text { S (Sprint Nextel) } & \$ 2.59 & 0.01 \\\\\hline \text { Non-Tech Stocks } & & \\\\\hline \text { DIS (Walt Disney) } & \$ 22.31 & -0.59 \\\\\hline \text { DUK (Duke) } & \$ 15.27 & -0.14 \\\\\hline \text { ED (Con Ed) } & \$ 39.66 & 0.20 \\\\\hline \text { FE (First Energy) } & \$ 48.90 & 1.14 \\\\\hline \text { MO (Altria Group) } & \$ 15.48 & 0.38 \\\\\hline \text { NVS (Novarnis) } & \$ 48.16 & -1.46 \\\\\hline\end{array}$$ On the morning of January 9,2009 , Swift advised your friend to purchase a collection of three stocks chosen at random from those listed in the table. Your friend was to sell all the stocks at the end of the trading day. a. How many possible collections are possible? b. How many of the collections in part (a) included exactly two tech stocks that increased in value by the end of the day? c. Using the answers to parts (a) and (b), what would you say the chances were that your friend chose a collection that included exactly two tech stocks that increased in value by the end of the day?
Calculate how many different sequences can be formed that use the letters of each given word. [Decide where, for example, all the s's will go, rather than what will go in each position. Leave your answer as a product of terms of the form \(C(n, r) .]\) Megalomania
Ben and Ann are among seven contestants from which four semifinalists are to be selected. Of the different possible selections, how many contain neither Ben nor Ann? (A) 5 (B) 6 (C) 7 (D) 14 (E) 21
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?
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