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Chapter 11: Problem 5
In Exercises 5-20, use the formula for \({ }_{n} C_{r}\) to evaluate each expression. \({ }_{6} C_{5}\)
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In Exercises 13-32, evaluate each factorial expression. \(\frac{9 !}{6 !}\)
If a single die is rolled twice, find the probability of rolling an odd number and a number greater than 4 in either order.
Write a probability problem involving the word "and" whose solution results in the probability fractions shown. \(\frac{1}{6} \cdot \frac{1}{6} \cdot \frac{1}{6}\)
The tables in Exercises 3-4 show claims and their probabilities for an insurance company. a. Calculate the expected value and describe what this means in practical terms. b. How much should the company charge as an average premium so that it breaks even on its claim costs? c. How much should the company charge to make a profit of \(\$ 50\) per policy? PROBABILITIES FOR HOMEOWNERS' INSURANCE CLAIMS $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Amount of Claim (to the } \\ \text { nearest } \$ \mathbf{\$ 5 0 , 0 0 0 )} \end{array} & \text { Probability } \\ \hline \$ 0 & 0.65 \\ \hline \$ 50,000 & 0.20 \\ \hline \$ 100,000 & 0.10 \\ \hline \$ 150,000 & 0.03 \\ \hline \$ 200,000 & 0.01 \\ \hline \$ 250,000 & 0.01 \\ \hline \end{array} $$
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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