Perms and Combs, Videos attached

Permutations and combinations are often misused and interchanged comfortably, along with arrangements, collections and groupings. It’s often easy to misuse them, but there is a slight difference in their meanings:

Permutations: An arrangement of a set of events or objects, where in the order of the events MATTERS.

Example: The arrangement of the numbers 1, 2, 3 and 1, 3, 2 is a different PERMUTAION.

Combinations: An arrangement of a set of events or objects, where in the order DOES NOT MATTER.

Example (follow-up): The arrangement of the numbers 1, 2, 3 and 1, 3, 2 is THE SAME COMBINATION.

The knowledge of the difference of meaning in these concepts is crucial.

There are different mathematical formulas for calculating permutation and combination arrangements. It is very important, however, to be able to logically analyze if the order in the arrangement matters.

For permutations:

 For combinations:

The only difference between the two is that in the combination formula, it is essential to divide the result by the number of ways the objects or events can inter-arrange to switch their order, because the order is irrelevant.

The following videos provide a very helpful visual guide to help further develop an understanding of these concepts:

http://www.khanacademy.org/math/probability/v/permutations-and-combinations-1

http://www.khanacademy.org/math/probability/v/permutations-and-combinations-2

http://www.khanacademy.org/math/probability/v/permutations-and-combinations-3

http://www.khanacademy.org/math/probability/v/permutations-and-combinations-4