Question

How many ways can 8 books be arranged on a shelf? Show all of your work for full credit.

Answer 1

Answer:

40,320.

Step-by-step explanation:

We are asked to find the number of ways in which 8 books could be arranged on a shelf.

The 1st could be arranged in 8 ways. Since one place is filled, so 2nd book could be arranged in 7 ways.

Similarly, the 3rd book could be arranged in 6 ways as first two places are already taken. This process will go on.

So the 8 books can be arranged in $8\times 7 \times 6\times5\times4\times3\times2\times1=8!$

$8!=40,320$

Therefore, 8 books could be arranged in 40,320 ways.

Answer 2

The number of ways to arrange 8 books on a shelf is 40,320.

We have to determine

How many ways can 8 books be arranged on a shelf?

According to the question

There is total number of books is 8.

Then,

The arranging the way of 8 books also be 8.

If one of the 8 books is placed in the first place, only 7 of them can be placed in 2nd place. In 3rd place, only 6 of them can be placed.

This continues all the way to 1.

A permutation is an arrangement of objects in a particular way.

Then,

The number of ways to arrange 8 books on a shelf is,

$= 8!\\ \\ = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\\ \\ =40,320$

Hence, The number of ways to arrange 8 books on a shelf is 40,320.

To know more about Permutation click the link given below.

https://brainly.com/question/7957549