John could not decide in what order to place his 7 books on his new shelf. How many ways can the 7 books be arranged?

The 7 books can be arranged in 5040 ways.

Step-by-step explanation:

It is given that,

John has 7 books and he has not decided to arrange the books in order.

So, you need to find out how many ways he could arrange his 7 books.

The first place can be filled up by any one of the 7 books.

Having filled the first place with any one of the 7 books we are left with 6 books.

The second place now can be filled up by any on of 6 books and so on.

This process gets repeated until no books are left.

We can thus fill up all the 7 places in 7 (6) (5) (4) (3) (2) (1) = 7!

⇒ 7! = 7*6*5*4*3*2*1

⇒ 5040 ways.

Hence, we can arrange 7 different books on a shelf in 5040 ways.