Problem 58
Question
Solve by the method of your choice. A book club offers a choice of 8 books from a list of \(40 .\) In how many ways can a member make a selection?
Step-by-Step Solution
Verified Answer
The number of ways a member can make a selection of 8 books from a list of 40 is given as the evaluated value of \(C(40, 8)\).
1Step 1: Identify the Parameters for the Combination Formula
Here, the total number of books (\(n\)) is 40 from which a member needs to make a choice of 8 books (\(r\)).
2Step 2: Apply the Combination Formula
Using the combination formula \(C(n, r) = \frac{n!}{r!(n-r)!}\), we substitute \(n = 40\) and \(r = 8\). The calculation becomes: \(C(40, 8) = \frac{40!}{8!(40-8)!}\).
3Step 3: Calculate the Factorials
Solve \(40!\), \(8!\), and \((40-8)!\) to get the respective values.
4Step 4: Substitute the Factorial Values Into the Formula
Substitute the calculated factorial values into the combination formula. Therefore, \(C(40, 8)\) equals the calculated value.
5Step 5: Evaluate the Expression
Perform the calculations in the numerator and the denominator, and then divide to evaluate the expression, thus obtaining the final answer.
Other exercises in this chapter
Problem 57
Let $$ \begin{array}{l} \left|a_{n}\right|=-5,10,-20,40, \ldots \\\ \left|b_{n}\right|=10,-5,-20,-35, \ldots \end{array} $$ and $$ \left\\{c_{n}\right\\}=-2,1,-
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Express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. $$a+a r+a r^{2}+\dots+a r^{12}$$
View solution Problem 58
Explain how to find the probability of an event not occurring. Give an example.
View solution Problem 58
Express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. $$a+a r+a r^{2}+. . . +a r^{12}$$
View solution