With origin in the Latin combinatio, combination is a word that refers to the act and consequence of combining something or combining (that is, joining, complementing or assembling different things to achieve a compound). The concept has multiple applications since the things that can be combined are of very different characteristics and origins.
A combination, according to theory, is understood as an ordered sequence of signs (which can be letters and / or numbers) only known to one or a few individuals and that allows certain mechanisms to be opened or put into operation. The locks and safes are, for example, devices that include combinations. For example: “I am going to give you the combination of the box but, please, keep the information safe”, “We cannot enter as this door is padlocked and I do not know the combination”, “Someone stole the combination and opened the safe, since the money is missing but it is not forced ”.
Of course, the idea of combination can also refer to the mixture or mixture of colors in the same unit. When dressing, a person usually chooses garments whose colors match, that is, they are harmonious in sight. For example: “I do not like this combination: I am going to choose shoes in another color”, “I cannot use that bag as it destroys the combination I chose for tonight”.
Likewise, the drink formed from the mixture of several liquors is known as a combination or drink: “Try this: it is a combination of blue curacao, grand marnier and champagne”, “It is a very strong combination, do not drink so fast”.
Concept in mathematical terms
In mathematics, on the other hand, we speak of combination when we focus on the subsets made up of a certain number of elements of a finite set analyzed and that differ by at least one element.
Generally we use the term to refer both to elements that are mixed regardless of the order, and those in which the order does matter; however, there is a way to name each of these mixes. 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, it does not matter the order in which we put the elements; On the other hand, if we want to mention the key to open a padlock, it is extremely important in what order we say the numbers. In mathematics there is a law that says:
If the order doesn’t matter, it’s a combination. If order does matter, it’s 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 doing a race, they cannot be taken at the the first and second years, nor the second before the first).
There is a formula for each of these types of mixtures that allows calculating how many possible results exist, these are:
For the permutations with repetition, n × n ×… (r times) = nr is used 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 should choose only 3; then the formula would be: 10 × 10 ×… (3 times) = 103 = 1000 permutations
For permutations without repetition the calculation is different because it must be taken into account what are the things you have to choose from and the only thing you have to remember is that you cannot repeat it. For example: if you are playing pull and have removed the 14 ball from the table, you will no longer be able to use it again in that game.