Question

In how many ways can 6 books be arranged on a shelf?

Answer 1

For the book standing on the left you have a choice out of all `6`, for the next one you choose from the `5` left, and so on.

Explanation:

So the total number of arrangements you have:

`6xx5xx4xx3xx2xx1=720`

Usually this is written as `6!`, pronounced "6 factorial"
(factorial meaning the product of all whole numbers from `1` up to and including the one before the `!`)

Answer 2

`6!` or `720` ways

Explanation:

For `6` books, that means we have `6` spots to put them in.

Our first book has `6` spots it can be in.

Our second book will now have `5`, since one is taken up by the first spot.

The next will have `4`, then `3`, `2`, and `1`. Thus, we can model the number of arrangements as

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

Therefore, we have `720` ways of arranging `6` books on the shelf.

Hope this helps!