Factorial Function
Introduction
Introduction
n! refers to the factorial function of a positive integer, n.
n! refers to the factorial function of a positive integer, n.
n! is defined as the product of all positive integers smaller than n.
n! is defined as the product of all positive integers smaller than n.
Visual Interpretation
Visual Interpretation
One way of interpreting n! is that you can think of it as the number of ways to arrange n distinct objects in a sequence (Permutations).
One way of interpreting n! is that you can think of it as the number of ways to arrange n distinct objects in a sequence (Permutations).
For example, 3! is equivalent to the number of ways to arrange 3 distinct letters (A, B, C) which is 6 ways.
For example, 3! is equivalent to the number of ways to arrange 3 distinct letters (A, B, C) which is 6 ways.
Explore!
Explore!
Use the applet below to explore the values of n! from 0 to 9.
Use the applet below to explore the values of n! from 0 to 9.
Why is 0! = 1?
Why is 0! = 1?
There are 2 ways to interpret 0! = 1.
There are 2 ways to interpret 0! = 1.
Method 1: If we use the permutation idea of factorials, 0! refers to the number of ways to arrange zero items. There is exactly 1 way. Do nothing.
Method 1: If we use the permutation idea of factorials, 0! refers to the number of ways to arrange zero items. There is exactly 1 way. Do nothing.