PERMUTATIONS Meaning and
Definition
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Permutations refer to the various ways or arrangements in which a set of distinct elements can be ordered or rearranged. In mathematics, permutations are commonly used to determine the total number of possible outcomes when selecting or arranging objects or elements.
A permutation comprises a specific ordering of the given set of objects. Each arrangement within a permutation is unique, and every element within the set is used exactly once.
To calculate the number of permutations, various methods can be employed, such as factorial notation or formulae. The factorial of a natural number, denoted by an exclamation mark (!), represents the product of all positive integers up to that number. For instance, if there are n distinct elements, then the number of permutations denoted as n!, would be multiplied together as n × (n-1) × (n-2) × ... × 3 × 2 × 1.
Permutations are utilized in a plethora of fields, including combinatorics, probability, statistics, computer science, and cryptography. They often play a vital role in solving problems related to arranging objects in a particular order or determining the possible outcomes of an event.
For example, in a lottery game where six balls are drawn from a set of 49, the total number of permutations would represent the number of different ways the six balls can be arranged in order. This concept of permutations finds practical applications not only in mathematics but also in various real-world scenarios.
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Etymology of PERMUTATIONS
The word "permutation" originates from the Latin term "permutatio", which comes from the verb "permuto" meaning "to change", "to exchange", or "to alternate". The Latin term itself is a combination of "per" meaning "through" or "thoroughly", and "mutare" meaning "to change" or "to exchange". Therefore, the etymology indicates that "permutations" refer to a thorough or thoroughgoing change or rearrangement.
Similar spelling words for PERMUTATIONS
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