Question

You need to arrange 10 of your favorite books on a small shelf. How many different ways can you arrange the books, assyming that the ordwr of the books make a differe

Answer 1

Answer:

You can arrange the books 3,628,800 different ways.

Step-by-step explanation:

You can imagine that the shelf has 10 "slots" where you can place a book. Each slot can take 1 of the 10 books. However, after you have placed 1 book, there are only 9 possible books to place. After 2 have been placed, there are only 8 possible.

Going left-to-right, the first slot has 10 available books.

Total combinations: 10

The 2nd slot has 9 available books.

Total combinations: 10 * 9

The 3rd slot has 8 available books.

Total combinations: 10 * 9 * 8

This continues for all 10 slots.

Eventually, for slot 10, there is only 1 book possible.

Total combinations: 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

Multiply all numbers between 10 and 1 with each other is also known as "10 factorial" or "10!"

Thus, the total number of combinations is:

$10! = 10*9*8*7*6*5*4*3*2*1 = 3628800$

Answer: You can arrange the books 3,628,800 different ways.