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Chapter 8: Problem 78
Use a calculator's factorial key to evaluate each expression. $$\frac{20 !}{300}$$
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Explain how to find the sum of the first \(n\) terms of a geometric sequence without having to add up all the terms.
Evaluate the given binomial coefficient. $$ \left(\begin{array}{l}8 \\\3\end{array}\right) $$
a. If two people are selected at random, the probability that they do not have the same birthday (day and month) is \(\frac{255}{365} \cdot \frac{364}{368} .\) Explain why this is so. (Ignore leap years and assume 365 days in a year.) b. If three people are selected at random, find the probability that they all have different birthdays. c. If three people are selected at random, find the probability that at least two of them have the same birthday. d. If 20 people are selected at random, find the probability that at least 2 of them have the same birthday. e. How large a group is needed to give a 0.5 chance of at least two people having the same birthday?
Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (2 x+1)^{4} $$
Find the term indicated in each expansion. \(\left(x^{2}+y\right)^{22} ;\) the term containing \(y^{14}\)
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