Permutation is a mathematical concept that refers to the arrangement of objects in a particular order. It is a simple yet powerful concept that has been used in various fields of mathematics and computer science. In this article, we will discuss what permutation is, its types, and how it is calculated.
What is Permutation?
Permutation refers to the arrangement of objects in a particular order. For example, if we have three objects A, B, and C, the possible permutations are ABC, ACB, BAC, BCA, CAB, and CBA. The order of the objects matters in a permutation. In other words, the arrangement ABC is different from BAC or CBA.
Types of Permutation
There are two types of permutation: with repetition and without repetition.
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Permutation with repetition: In permutation with repetition, the objects can be repeated. For example, if we have two objects A and B, the possible permutations with repetition are AA, AB, BA, and BB.
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Permutation without repetition: In permutation without repetition, the objects cannot be repeated. For example, if we have two objects A and B, the possible permutations without repetition are AB and BA.
Calculating Permutation
The formula for calculating permutation is:
P(n, r) = n! / (n-r)!
Where P is permutation, n is the total number of objects, and r is the number of objects in each permutation.
For example, if we have five objects A, B, C, D, and E, and we want to find the number of permutations of three objects, we can use the formula:
P(5,3) = 5! / (5-3)!
= 5! / 2!
= 5 x 4 x 3
= 60
Therefore, there are 60 possible permutations of three objects from a set of five objects.
Conclusion
Permutation is a fundamental concept in mathematics and computer science that has various applications. It is used in cryptography, coding theory, combinatorics, and many other fields. Permutation helps to determine the number of possible outcomes of a particular event, which is essential in decision-making and probability. Understanding permutation is crucial for students and professionals in mathematics and computer science.