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Chapter 33: Problem 1062

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

Short Answer

Expert verified
There are 6 ways to arrange the 3 books next to each other on a shelf.

Step by step solution

01

1. Identify the number of choices at each step

For the first book, you have 3 choices to place on the shelf, as you can choose any of the 3 books. For the second book, after placing the first book, you only have 2 books left to choose from, so you have 2 choices. Finally, for the third book, you only have 1 book left, so you have only 1 choice.
02

2. Calculate the total number of arrangements

The total number of ways to arrange the books is the product of the number of choices at each step. So, we would multiply the choices we got in step 1: Number of arrangements = Number of choices for the first book 脳 Number of choices for the second book 脳 Number of choices for the third book Number of arrangements = 3 脳 2 脳 1
03

3. Simplify the result

Now, multiply the numbers we have: Number of arrangements = 3 脳 2 脳 1 = 6 So, there are 6 ways to arrange the 3 books next to each other on a shelf.

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