Permutation and Combination

A permutation is an ordered arrangement of objects (order does matter).

A combination is the unordered arrangement of objects (order doesn’t matter).

We use the permutation and combination formulas to find the total number of items can be selected from the sample.

Permutation formula:

Combination formula:

These formulas can be easily find online too.

where n is the total number of items in the sample, and r is the number of items to be selected from the sample.

Notice:   k! = k(k-1)(k-2)(k-3)…(3)(2)(1).

To distinguish the different between permutation and combination is very important because the answer will be wrong if apply the wrong formula.

Here are the examples of the permutation and combination:

1.  In a group of 20 people, in how many way we can choose a President, a vice President, and a Secretary?                                                                                                           —This problem is a permutation problem, because President, Vice President, and Secretary are different, so the order does matter. So the solution for this problem will be: P(20,3) = 6840 different way to select the 3 out of 20 people to assign 3 different roles.
2. In how many way can we form a 3-person committees?                                                             This problem is a combination problem because there is no different between the committees. A committee is a committee, it doesn’t matter which one we choose first, it makes no different. So the answer to this problem will be:                                        C(20,3) =  1140 different way.