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Chapter 21: Problem 500

In how many ways may 3 books be placed next to each other on a shelf?

Short Answer

Expert verified
There are \(6\) different ways to arrange the 3 books on the shelf.

Step by step solution

01

Identify the permutation formula

To find the number of ways to arrange given objects, we use the permutation formula: nPr = n! / (n-r)!, where n is the total number of objects, r is the number of objects being arranged, and nPr is the number of permutations.
02

Apply the permutation formula to the given problem

In our problem, we have 3 books to be arranged in a row (n=3), and we need to arrange all of them (r=3). Thus, the formula now becomes: 3P3 = 3! / (3-3)!
03

Calculate the factorials

Now, we need to calculate the factorials: 3! = 3 脳 2 脳 1 = 6 (3-3)! = 0! = 1 (by definition, 0! = 1)
04

Substitute the factorials back into the formula

Now, we can substitute the calculated factorials back into our formula: 3P3 = 6 / 1
05

Calculate the number of permutations

Finally, we can complete the calculation and find the number of permutations: 3P3 = 6 So, there are 6 different ways to arrange the 3 books on the shelf.

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