Even Permutations Calculator

Instructions:
  • Enter the number of elements (n > 2) in the input field below.
  • Click "Calculate" to calculate the even permutations.
  • Click "Clear" to clear the input and result.
  • Click "Copy Result" to copy the result to the clipboard.
  • View the detailed calculation and explanation below.
  • Check the calculation history below for your previous results.
Result:
Detailed Calculation

Calculation History

    The Even Permutations Calculator is a tool that calculates the number of even permutations for a set of n elements where n > 2. It is a simple and easy-to-use tool that can be used to calculate the even permutations of any set of elements.

    Concepts

    Permutations

    A permutation is an arrangement of objects in a specific order. For example, the permutations of the set {1, 2, 3} are {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}. The number of permutations of a set of n elements is given by n!.

    Even Permutations

    An even permutation is a permutation that can be obtained from an even number of two-element swaps. For example, the permutation (1, 2, 3, 4) is an even permutation because it can be obtained from zero swaps. The permutation (1, 3, 4, 2) is also an even permutation because it can be obtained from two swaps.

    Odd Permutations

    An odd permutation is a permutation that can be obtained from an odd number of two-element swaps. For example, the permutation (1, 2, 3, 4) is not an odd permutation because it cannot be obtained from an odd number of swaps. The permutation (1, 3, 2, 4) is an odd permutation because it can be obtained from one swap.

    Factorials

    A factorial is the product of all positive integers up to a given number. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

    Formulae

    The formula for calculating the number of even permutations for a set of n elements where n > 2 is n! / 2. This formula is derived from the fact that half of all permutations are even and half are odd.

    Benefits

    The Even Permutations Calculator is a useful tool for anyone who needs to calculate the number of even permutations for a set of elements. It is particularly useful for students and professionals who work in fields such as mathematics, computer science, and engineering.

    Interesting Facts

    • The number of even permutations for a set of n elements is the same as the number of odd permutations.
    • The number of even permutations for a set of n elements is given by n! / 2.
    • The number of even permutations for a set of 4 elements is 12.
    • The number of even permutations for a set of 5 elements is 60.

    Last Updated : 11 December, 2023

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