The combination of a lock is the ordered sequence of letters and/or numbers that allows it to be opened.
Originating from 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 diverse things to achieve a compound ). The concept has multiple applications since the things that can be combined have very diverse characteristics and origins.
A combination, according to the theory, is understood as an ordered sequence of signs (which can be letters and/or numbers) only known by one or a few individuals and that allows certain mechanisms to be opened or put into operation. Padlocks and safes are, for example, devices that include combinations. For example: “I'm going to give you the combination to the box but please keep the information safe,” “We can't enter because this door is locked and I don't know the combination,” “Someone stole the combination and opened it. ” the safe, since the money is missing but it is not forced.”
Combination as a mix of colors or drinks
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 clothes whose colors match, that is, they are harmonious to the eye: “I don't like this combination: I'm going to choose shoes of a different color,” “I can't use that purse because 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, don't drink so quickly” .
When choosing clothes, we usually go for a harmonious combination.
The concept in mathematical terms
In mathematics , on the other hand, we speak of combination when we focus on subsets made up of a certain number of elements of a finite set analyzed and that differ in at least one element.
We generally use the term to refer to both 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 mixtures. One of them is combination, the other, permutation.
Combination and order
It is not the same if we want to refer to what is in a tomato, lettuce and onion salad, 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 lock, it is extremely important in what order we say the numbers. In mathematics there is a law that says:
«If the order does not matter, it is a combination.
If the order does matter, it is a permutation.
Therefore a permutation is a combination that is carried out 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 taking a race, they cannot be taken at the same time. once the first and the second year, nor the second before the first).
Permutation and formulas
There is a formula for each of these types of mixtures that allows you to calculate how many possible results there are, these are:
For permutations with repetition, n × n × … (r times) = nr is used Where n is the number of things you can choose and r is 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 must take into account what 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 you have removed ball 14 from the table, you will no longer be able to use it in that game.