Factorial method. What is the probability to have two girls and three boys in a family?
Factorial !
Example: 4! is shorthand for 4 x 3 x 2 x 1
Factorial Symbol
The factorial function (symbol: !) means to multiply a series of descending natural numbers. Examples:
4! = 4 × 3 × 2 × 1 = 24
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
1! = 1
4! is usually pronounced “4 factorial“, but some people even say “4 shriek“ or “4 bang“
Calculating From the Previous Value
You can easily calculate a factorial from the previous one:
n n!
1 1 1 1
2 2 × 1 = 2 × 1! = 2
3 3 × 2 × 1 = 3 × 2! = 6
4 4 × 3 × 2 × 1 = 4 × 3! = 24
5 5 × 4 × 3 × 2 × 1 = 5 × 4! = 120
6 etc etc
Example: What is 10! if you know that 9!=362,880 ?
10! = 10 × 9!
10! = 10 × 362,880 = 3,628,800
So the rule is:
n! = n × (n-1)!
Which just says “the factorial of any number is that number times the factorial of (1 smaller than that number)“, hence 10! = 10 × 9!, or even 125! = 125 × 124!
What About “0!“
Zero Factorial is interesting ... it is generally agreed that 0! = 1.
It may seem funny that multiplying no numbers together gets you 1, but it helps simplify a lot of equations.
Where is Factorial Used?
Factorials are used in many areas of mathematics, but particularly in Combinations and Permutations
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