Difference Between Permutation and Combination

Permutation vs Combination

Permutations and combinations are both related mathematical concepts. Because they are related concepts, most of the time they are used with each other or switched or swapped with each other without realizing it. As mathematical concepts, they serve as precise terms and language to the situation they are describing or covering.

“Combination” is defined as the selection of objects, symbols, or values from a wide variety like a large group or a certain set with underlying similarities. In a combination, the importance is made on the choice of the objects or values themselves. One combination comprises one value plus another value (as a pair) with or without additional values (or as a multiple).

Values or objects in a combination do not require order or arrangement. The combination can also be random in nature. Also, the values or objects can be considered as alike or the same in comparison with each other. A combination, with relation to permutation, can be several in numbers while permutation can be less or single in comparison.

On the other hand, permutation is also the selection of objects, values, and symbols with careful attention to the order, sequence, or arrangement. Aside from giving an emphasis on these three things, permutation gives the values or objects’ destinations by virtue of assigning them into a specific placement with each other. For example, a certain value or a combination of values can be assigned as the first, second, and so on.
With respect to a combination, a permutation is basically an ordered or arranged combination. A permutation also deals with a number of ways to arrange, rearrange, and order the objects and symbols. One permutation is equal to a single arrangement or order. One arrangement or permutation is distinctly different from another arrangement or permutation.
Permutations and combinations are often used as word problems in mathematical textbook exercises. Another application is in data preparation and probability in research. Using “permutation” and “combination” can easily help to predict something with the given data.
Permutation has the formula: P(n,r). Meanwhile, finding the combination requires this particular mathematical method –
The (n,r) in the second permutation formula (which also applies when finding the combination) represents two things–the value of “n” is the initial number mentioned while the second value (which is r) is the times that the decreasing and succeeding value will be multiplied to the value of “n.”

Summary:

1.“Permutation” and “combination” are related mathematical concepts. “Combination” is any selection or pairing of values within a single criteria or category while “permutation” is an ordered combination.
2.Combinations do not place an emphasis on order, placement, or arrangement but on choice. Values can be single or paired. On the other hand, permutations place a high emphasis on the three aforementioned characteristics. Aside from these three, a permutation also gives the destination of each value (or paired value).
3.A number of permutations can be derived from a single combination. Meanwhile, one permutation calls for a single arrangement.
4.Permutations are often regarded as ordered elements while combinations are looked upon as sets.
5.A single permutation is distinct and different on its own and from each arrangement while a combination is often alike in comparison with other combinations.
6.Both “permutation” and “combination” are often used in math word problems and probabilities in statistics and research.

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