One such example would be the order of the first three runners in a race. × n 0! is defined to be 1.-Where the order of selection does matter, it is called a permutation. One such example is the UK's National Lotto where 6 numbers have to be chosen from the 59 numbers 1-59).If there are n different items and a subset of r of them are chosen where the order of choosing does not matter then the number of combinations is given by:nCr = n!/((n-r)!r!)where n! means "n factorial" - the product of all numbers 1 × 2 ×. Without repetition simply means that when one has drawn an element it cannot be drawn again, so with repetition implies that it is replaced and can be drawn again. One could say that a permutation is an ordered. The two key things to notice about permutations are that there is no repetition of objects allowed and that order is important. That suggests that it does not always hold in situations where multiplication does not commute - for example, the multiplication of a type of numbers known as quaternions is not commutative. Permutations can be denoted in a number of ways: n P r, n P r, P(n, r), and more. If the order doesnt matter then we have a combination, if the order do matter then we have a permutation. Of course this all relies on the central premise that multiplication commutes in the reals and thus ensures that the order of the factors does not matter. in a lottery it normally does not matter in which order the numbers are drawn). In cases where the order doesnt matter, we call it a combination instead. The grouping of a subset of a set of items where the order does not matter is called a combination. Permutation implies that the order does matter, with combinations it does not (e.g. What is a grouping of objects or events in which order does not matter?
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