Part 2/5:
To understand how many ways we can sort ( n ) distinct objects, let's consider a simple example of four letters: A, B, C, D. These can be arranged in all possible permutations, which we denote as 4 factorial (( 4! = 24 )).
When analyzing how these letters can be sorted, we can illustrate that the combinations generated from A, B, C, and D lead to 24 unique arrangements like:
A B C D
B A C D
A D C B
... (and so on)
General Proof for Sorting n Distinct Objects
Now, let's expand this concept to ( n ) distinct objects. We will use the example of numbers from 1 to ( n ).