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Originating in Latin combinatio, combination it is a word that refers to act and consequence of combining something or combining (that is, join, complement or assemble diverse things to achieve a compound ). The concept has multiple applications since the feasible things to combine are of very different characteristics and origins.

A combination, according to the theory, is understood as a ordered sequence from signs (which may be letters and / or numbers) known only to one or a few individuals and that allows certain mechanisms to be opened or put into operation. The padlocks and the safes they are, for example, devices that include combinations. For example: "I'm going to give you the combination of the box, but please keep the information in the safe", “We cannot enter since this door is locked and I don't know the combination”, "Someone stole the combination and opened the safe, since the money is missing but not forced".

Of course, the idea of ​​combination can also refer to the mixture or mixture from colors In the same unit. When dressing, a person usually choose garments whose colors combine, that is, they are harmonious in sight. For example: "I don't like this combination: I'm going to choose shoes of another color", “I can't use that wallet since it destroys the combination I chose for tonight”.

It is also known as a combination or drink at beverage formed from the mixture of various liquors : “Try this: it is a combination of blue curacao, grand marnier and champagne”, “It's a very strong combination, don't drink so fast”.

Concept in mathematical terms

In the mathematics On the other hand, there is talk of a combination when focusing on the subsets formed by a certain quantity of elements of a finite set analyzed and which differ in at least one element.

We generally use the term to refer to both elements that mix regardless of order, such as those in which order does matter; however, there is a way to name each of these mixtures. One of them is combination, the other, permutation.

It is not the same if we want to refer to what a tomato, lettuce and onion salad has, no matter the order in which we put the elements; On the other hand, if we want to mention the key to open a lock, it is extremely important in what order we say the numbers. In mathematics there is a law that says:

"If order does not matter, it is a combination.
If order does matter, it is a permutation. "

Therefore a permutation is a combination that is performed in a stipulated order. There are, however, two types of them: with repetition (which allow a number to be used more than once, for example: 666) or without repetition (They cannot be altered or repeated. For example, when making a career, they cannot take the first and second year at the same time, nor the second before the first).

There are for each of these types of mixtures a formula which allows to calculate how many possible results exist, these are:

For permutations with repetition it is used n × n ×… (r times) = nr Where n is the amount of things you can choose and r what you choose. For example: if you have to choose three numbers for a lock, you have 10 numbers to choose from (0,1,…, 9) and you must choose only 3; Then the formula would be: 10 × 10 ×… (3 times) = 103 = 1000 permutations

For permutations without repetition the calculation is different because you have to take into account what are the things you have to choose and all you have to remember is that you cannot repeat it. For example: if you are playing pull and have eliminated ball 14 from the table, you will not be able to use it again in that game.

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