Part 4/5:
Factorials are prevalent in many areas of mathematics, particularly in combinatorics. They are used to determine the number of ways to arrange distinct objects.
Arranging Items
To understand this concept, let’s consider sorting a set of four letters: A, B, C, and D. The total ways to sort 4 distinct letters is calculated as:
- 4! = 4 × 3 × 2 × 1 = 24 ways.
To illustrate how this works, we can structure the process of sorting these letters.
Proof of Sorting
Starting with ABCD, you can rearrange them by fixing one letter and permuting the others.
Fix A: A can be followed by B, C, D in multiple configurations.
For each of these configurations, the next letter can be fixed and the remaining permuted.