How to Calculate Inverse Factorial

The inverse factorial is simply the inverse of the factorial. The factorial exists for 0 and all positive integers, and is usually written with an exclamation mark; that is, the factorial of 6 is written "6!"



The factorial of 0 is defined as 1. The factorial of any positive integer is the product of all integers less than or equal to that integer. For example 6! = 6 * 5 * 4 * 3 * 2 * 1. Inverse factorials are used in probability and statistics.

Instructions

1. Determine if the number in the factorial is 0 or 1. If it is, then the factorial is 1. That is 0! = 1! = 1.

2. Multiply the number in the factorial by the number that is 1 smaller than it, if the number is not 0 or 1. For example, if you want the inverse of 6!, multiply 6 by 5 to get 30.

3. Repeat Step 2 until you get to 1. This gives you the factorial. In the example;

   30*4 = 120

   120*3 = 360

   360*2 = 720

   720*1 = 720.

4. Take the inverse of the result from Step 1 or Step 3. To do this, divide 1 by the result. This is the inverse factorial. For example, the inverse factorial of 0 is 1/1 = 1. The inverse factorial of 6 is 1/720 = 0.0014.

Tips & Warnings

• Many calculators have buttons for factorial and inverse.

References

• Physics forums: Inverse factorials