In mathematics, disordered groups are called sets and subsets. The elements are not repeated, and it does not matter the order of the group's elements. k m ! n ! Ī typical example is to find out how many seven-digit numbers formed from the numbers 2,2,2, 6,6,6,6.Ī combination of a k-th class of n elements is an unordered k-element group formed from a set of n elements. Repeating some (or all in a group) reduces the number of such repeating permutations. n = n kĪ repeating permutation is an arranged k-element group of n-elements, with some elements repeating in a group. We calculate their number according to the combinatorial rule of the product: A typical example is the formation of numbers from the numbers 2,3,4,5, and finding their number. 1 = n !Ī typical example is: We have 4 books, and in how many ways can we arrange them side by side on a shelf?Ī variation of the k-th class of n elements is an ordered k-element group formed of a set of n elements, wherein the elements can be repeated and depends on their order. The elements are not repeated and depend on the order of the elements in the group. It is thus any n-element ordered group formed of n-elements. The permutation is a synonymous name for a variation of the nth class of n-elements. For calculations, it is fully sufficient to use the procedure resulting from the combinatorial rule of product. The notation with the factorial is only clearer and equivalent. N! we call the factorial of the number n, which is the product of the first n natural numbers. For example, if we have the set n = 5 numbers 1,2,3,4,5, and we have to make third-class variations, their V 3 (5) = 5 * 4 * 3 = 60. The number of variations can be easily calculated using the combinatorial rule of product. The elements are not repeated and depend on the order of the group's elements (therefore arranged). C k ( n ) = ( k n ) = k ! ( n − k ) ! n ! n = 1 0 k = 4 C 4 ( 1 0 ) = ( 4 1 0 ) = 4 ! ( 1 0 − 4 ) ! 1 0 ! = 4 ⋅ 3 ⋅ 2 ⋅ 1 1 0 ⋅ 9 ⋅ 8 ⋅ 7 = 2 1 0 The number of combinations: 210Ī bit of theory - the foundation of combinatorics VariationsĪ variation of the k-th class of n elements is an ordered k-element group formed from a set of n elements.
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