Permutations and Combinations Compared

In probability and statistics, combinations  and permutations are the two primary concepts to count how many ways a set of items can be selected or arranged. The fundamental difference between them comes down to one thing: order. If the order doesn't matter, it is a combination. If the order does matter, it is a permutation.

I. Intro to Combinations and Permutations
A. Combinations (Order Does Not Matter)
A combination is a selection of items where the sequence is irrelevant. You are only concerned with which items are picked, not how they are arranged.

A simple example would be a fruit salad. A mix of apples, grapes, and bananas is the same salad as bananas, grapes, and apples. The group is the same regardless of what went into the bowl first.

There are basically two types of combinations:

1. Combinations without Repetition

2. Combinations with Repetition

B. Permutations (Order Matters)
A permutation is an arrangement of items where the specific sequence is important. If you change the order of the items, you have a new permutation. 

A simple example would be a door lock code. If the code is 1-2-3, entering 3-2-1 will not open the door. Even though the numbers are the same, the order makes them a distinct "arrangement."

There are basically two types of permutations:

1.Permutations without Repetition

2. Permutations with Repetition

CK-12: Permutations and Combinations Compared

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https://www.mathsisfun.com/combinatorics/combinations-permutations.html

https://virtuallearningacademy.net/LessonDisplay/Lesson6243/MATHALGIIBU33Probability_Combinations.pdf

https://www.geeksforgeeks.org/maths/permutations-and-combinations/