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Chapter 11: Problem 17
Evaluate each factorial expression. \(\frac{19 !}{11 !}\)
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How many four-digit odd numbers are there? Assume that the digit on the left cannot be 0 .
As in Exercise 1, six performers are to present their comedy acts on a weekend evening at a comedy club. One of the performers insists on being the last stand-up comic of the evening. If this performer's request is granted, how many different ways are there to schedule the appearances?
In the original plan for area codes in 1945 , the first digit could be any number from 2 through 9 , the second digit was either 0 or 1 , and the third digit could be any number except 0 . With this plan, how many different area codes are possible?
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?
A camp counselor and six campers are to be seated along a picnic bench. In how many ways can this be done if the counselor must be seated in the middle and a camper who has a tendency to engage in food fights must sit to the counselor's immediate left?
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