You may rearrange the 6 books on the shelf in different ways and you may find the number of permutations using factorial formula such that:

`n! = 1*2*3*...*(n-2)*(n-1)*n`

Hence, reasonign by analogy yields:

`6! = 1*2*3*4*5*6 => 6! = 720`

**Hence, since the problem does not indicate to arrange a given number of books, out of all 6, on the shelf, then you only may solve the problem using permutation `6! = 720` .**

The answer is indeed 6!=720, but those are **permutations**. Combinations would be if you were asked in how many ways can you choose eg. 2 out of 6 books. In that case the answer would be `6 choose 2 = (6 cdot 5)/(1 cdot 2) = 15.`

Note: number of permutations = number of arrangements.

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now