difference between permutation and combination with example by geeksforgeek
Answers
1. The term permutation refers to several ways of arranging a set of objects in a sequential order. Combination implies several ways of choosing items from a large pool of objects, such that their order is irrelevant.
2. The primary distinguishing point between these two mathematical concepts is order, placement, and position,i.e. in permutation characteristics mentioned above does matter, which does not matter in the case of the combination.
3. Permutation denotes several ways to arrange things, people, digits, alphabets, colours, etc. On the other hand, combination indicates different ways of selecting menu items, food, clothes, subjects, etc.
4. The permutation is nothing but an ordered combination while Combination implies unordered sets or pairing of values within specific criteria.
5. Many permutations can be derived from a single combination. Conversely, a single combination can be obtained from a single permutation.
6. Permutation answers How many different arrangements can be created from a given sets of objects? As opposed to the combination which explains How many different groups can be picked from a larger group of objects?
EXAMPLE
Suppose, there is a situation where you have to find out the total number of possible samples of two out of three objects A, B, C. In this question, first of all, you need to understand, whether the question is related to permutation or combination and the only way to find this out is to check whether the order is important or not.
If the order is significant, then the question is related to permutation, and possible samples will be, AB, BA, BC, CB, AC, CA. Where AB is different from BA, BC is different from CB and AC is different from CA.
If the order is irrelevant, then the question is related to combination, and the possible samples will be AB, BC and CA.
