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Chapter 11: Problem 59
Explain the best way to evaluate \(\frac{900 !}{899 !}\) without a calculator.
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For a temporary job between semesters, you are painting the parking spaces for a new shopping mall with a letter of the alphabet and a single digit from 1 to 9 . The first parking space is \(\mathrm{A} 1\) and the last parking space is Z9. How many parking spaces can you paint with distinct labels?
Consider a political discussion group consisting of 5 Democrats, 6 Republicans, and 4 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting no Independents.
Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. An apartment complex offers apartments with four different options, designated by A through D. There are an equal number of apartments with each combination of options. $$ \begin{array}{|l|l|l|l|} \hline \text { A } & \text { B } & \text { C } & \text { D } \\ \hline \text { one bedroom } & \text { one } & \text { first } & \text { lake view } \\ \text { two bedrooms } & \text { bathroom } & \text { floor } & \text { golf course } \\ \text { three } & \text { two } & \text { second } & \text { view } \\ \text { bedrooms } & \text { bathrooms } & \text { floor } & \text { no special } \\ & & & \text { view } \\ \hline \end{array} $$ If there is only one apartment left, what is the probability that it is precisely what a person is looking for, namely two bedrooms, two bathrooms, first floor, and a lake or golf course view?
In Exercises 43-48, an ice chest contains six cans of apple juice, eight cans of grape juice, four cans of orange juice, and two cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting three cans of apple juice.
Evaluate each factorial expression. \(\frac{12 !}{10 !}\)
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