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Chapter 11: Problem 42

A book club offers a choice of 8 books from a list of 40 . In how many ways can a member make a selection?

Short Answer

Expert verified
The member can make a selection in 76,904,685 different ways.

Step by step solution

01

Identify the problem type

This is a combination problem, as the order of selection does not matter, only the choice of the items. Combination is given by the formula: \( \binom{n}{r} = \frac{n!}{r!(n - r)!} \), where \( n \) is the total number of items, \( r \) is the number of items to choose, and \( ! \) indicates factorial, which is the product of all positive integers up to that number.
02

Insert the given numbers

In this case, \( n = 40 \) (the total number of books), and \( r = 8 \) (the number of books to choose). Substitute these values into the formula: \( \binom{40}{8} = \frac{40!}{8!(40 - 8)!} \)
03

Compute Factorials

First, calculate the factorial values. 8! = 40,320 and 32! is a very large number, we suggest to use a calculator or a software to compute it. The simplified form of 40! is already computed by the calculator.
04

Compute the Combination

Use these factorial values in the combination formula. Substitute \( \frac{40!}{8! * 32!} \) in the calculator to find the final result.

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