Combinatorics is a branch of mathematics that is dedicated to counting and classifying the possible arrangements of a set of elements. Two important concepts in combinatorics are permutation y combination. Next, we will explain what each one consists of and what the difference is between them.

Permutation

A permutation is an ordered arrangement of elements of a set in which all elements are taken into account and the order in which they are placed matters. In other words, it is a factorial of a finite number of objects, in which all possible ways of ordering them are taken into account.

Permutation formula

The formula to calculate the permutation of a set of n elements taken from r en r is:

nPr = n! / (nr)!

Permutation example

Let's take as an example a set of three letters: A, B and C. If we want to find all permutations of 2 letters taken from this set, we would use the above formula:

3P2 = 3! / (3-2)! = 3

Therefore, the possible permutations are: AB, AC, BA, BC, CA and CB.

Combination

A combination is an unordered arrangement of elements of a set in which some elements are taken into account and the order in which they are placed does not matter. In other words, subsets of a set can be formed and the order of the elements in each subset is not relevant.

combination formula

The formula to calculate the combination of a set of n elements taken from r en r is:

nCr = n! /r!(nr)!

Combination example

Let's take as an example the same set of three letters: A, B and C. If we want to find all combinations of 2 letters taken from this set, we would use the above formula:

3C2 = 3! / 2!(3-2)! = 3

Therefore, the possible combinations are: AB, AC and BC.

Difference between permutation and combination

The main difference between permutation and combination is the order in which the elements are taken. In permutation, the order is relevant while in combination it is not. Furthermore, in permutation all the elements of the set are taken into account while in combination only a subset of them is taken.

Conclusion

Permutation and combination are two basic concepts in combinatorics. It is important to know the difference between them to be able to use them correctly in various mathematical and statistical problems.

References

• https://es.wikipedia.org/wiki/Permutaci%C3%B3n
• https://es.wikipedia.org/wiki/Combinaci%C3%B3n

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