What is a Factorial?
- A factorial, indicated by an exclamation mark, is a number multiplied by all the integer numbers before it.
- This means that the factorial of x, x!, would be:
x! = x * (x-1) * (x-2) * (x-3) * (x-4) * ..... * 1
- Where x is multiplied by all the values preceding x until one.
- The first few factorials are:
- From here we can see that factorials get big quick!
- A factorial is defined as:
- A neat trick with factorials is that the factorial for a value is the same as that value multiplied by the factorial for that value minus 1!
x! = x * (x-1)! = x * (x-1) * (x-2)!
Purpose of Factorials
- A factorial shows the number of ways a number of objects can be arranged.
- Thus the number of ways of arranging n distinct objects in a row is n!.
- Factorials are essential in calculating probabilities.
- They are used in the formulae for permutations and combinations.
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