What Is Permutation And Combination?
What is Permutation and Combination?
Permutation and Combination are two areas of mathematics related to the arrangement of objects in different ways. Permutation is the arrangement of objects in a specific order, while combination is the selection of objects without any particular order. Both of these topics are applicable in various fields, such as probability, combinatorics, algebra, and even computer programming.
Permutations
A permutation is the arrangement of objects in a particular order. It is the number of ways that a certain number of objects can be arranged. For example, the permutations of the word “CAT” would be “CAT”, “ACT”, “ATC”, “TCA”, “TAC”, and “CTA”. The number of permutations of n objects is n! (n factorial).
Combinations
A combination is the selection of objects without any particular order. It is the number of ways that a certain number of objects can be selected from a larger set. For example, the combinations of the letters A, B, and C would be A, B, C, AB, AC, BC, and ABC. The number of combinations of n objects taken r at a time is given by the formula nCr = n!/[r!(n-r)!].
Examples of Permutation and Combination
Example 1: Permutations
Find the number of permutations of the word “HELLO”.
Solution: The number of permutations of the word “HELLO” is 5! = 120.
Example 2: Combinations
Find the number of combinations of the letters A, B, C, and D taken two at a time.
Solution: The number of combinations of the letters A, B, C, and D taken two at a time is 4C2 = 6.
Conclusion
Permutation and combination are two areas of mathematics related to the arrangement and selection of objects. Permutation is the arrangement of objects in a specific order, while combination is the selection of objects without any particular order. Both of these topics are applicable in various fields, such as probability, combinatorics, algebra, and even computer programming.
In this article, we discussed what permutation and combination are, how they are related, and how to calculate the number of permutations and combinations. We also provided some examples of permutation and combination to help you understand the concepts better.
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