# Suppose I had a shelf of 5 different books, and I wanted to know: in how many different orders can I put these 5 books? Another way to say that is: 5 books

have how many different permutations?

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have how many different permutations?

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In order to answer this question, we need an odd math symbol.

The factorial. It’s written as an exclamation sign, and it means:

The product of that number and all the positive integers below it, down to 1.

For example, 4! (read “four factorial“) is

4! = (4)(3)(2)(1) = 24

Here’s the permutation formula:

# of permutations of n objects = n!

So, five books the number of permutations is 5! = (5)(4)(3)(2)(1) = 120

Answer = 120

There are n! different ways of arranging n distinct objects into a sequence, the permutations of those objects.

(Spelled as n factorial)

At first, you have 5 different choices, so our first number in the multiplication problem will be 5. Now that one is missing, the number is reduced to 4. Next, it’s down to 3, and so on. So, the total number of ways to order the 5 books is

= (5)(4)(3)(2)(1)

= 120