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A factorial is a function that multiplies a number by every number below it. For example 5!= 5*4*3*2*1=120. The function is used, among other things, to find the number of way “N” objects can be arranged.

Instead of calculating out a factorial 1 digit at a time, use this calculator to calculate the factorial, n! of a number n. Enter an integer, up to 4 digits long, and choose if you want the full integer answer or abbreviated scientific notation. If you select the Full Integer Answer for large factorials, you may want to copy the result and paste it into another document to view it.

In mathematics, there are n! ways to arrange n objects in sequence. "The factorial n! gives the number of ways in which n objects can be permuted."[1] For example:

- 2 factorial is 2! = 2 x 1 = 2

-- There are 2 different ways to arrange the numbers 1 through 2. {1,2,} and {2,1}. - 4 factorial is 4! = 4 x 3 x 2 x 1 = 24

-- There are 24 different ways to arrange the numbers 1 through 4. {1,2,3,4}, {2,1,3,4}, {2,3,1,4}, {2,3,4,1}, {1,3,2,4} ..... etc. - 5 factorial is 5! = 5 x 4 x 3 x 2 x 1 = 120
- 0 factorial is a definition: 0! = 1. There is exactly 1 way to arrange 0 objects.

__Factorial Problem 1__: How many different ways can the letters in the word “Document” be arranged?

For this problem we simply take the number of letters in the word and find the factorial of that number. This works because each letter in the word is unique and we are simply finding the maximum amount of ways 8 items can be ordered.

8!=8*7*6*5*4*3*2*1= **40,320**

__Factorial Problem 2__: How many different ways can the letters in the word “physics” be arranged?

This problem is slightly different because there are two “s” letters. To account for this we divide by the number of duplicate letters factorial. There are 7 letters in the word physics and two duplicate letters so we must find 7!/2!. If the word had multiple duplicates, as in “little”, the formula would be 6!/(2!* 2!).

7!/2!=(7*6*5*4*3*2*1)/(2*1)= **2,520**

[1] For more information on factorials please see http://mathworld.wolfram.com/Factorial.html

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Furey, Edward "Factorial Calculator n!" From *http://www.CalculatorSoup.com* - Online Calculator Resource.