Permutation and Combination

 

A permutation is an arrangement of objects in a specific order, while a combination is a selection of objects where order doesn't matter.

Here's a simple way to think about it:

- Permutation: Imagine you have 3 letters, A, B, and C. You want to know how many different ways you can arrange them. You have 6 possible permutations: ABC, ACB, BAC, BCA, CAB, CBA.

- Combination: Now, imagine you have the same 3 letters, and you want to know how many different ways you can choose 2 letters. You have 3 possible combinations: AB, AC, BC. Notice that AB is the same as BA in this case, as order doesn't matter.

Key Differences:

- Order: Permutations consider order, while combinations do not.

- Formula: The formulas for calculating permutations and combinations are different:

- Permutation: nPr = n! / (n-r)! (where n is the total number of objects and r is the number of objects being arranged)

- Combination: nCr = n! / (r! * (n-r)!)

Example:

Let's say you have 5 friends, and you want to choose 3 of them to go to the movies.

- Permutation: If you want to know how many different ways you can arrange the 3 friends you choose (e.g., who sits in the front, middle, and back seat), you'd use a permutation.

- Combination: If you just want to know how many different groups of 3 friends you can choose, without considering the order, you'd use a combination.