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 Arithmetics Signed numbers Divisibility Decimals Fractions Percentages Proporcional reasoning Mixture problems Prime numbers Factoring Prime factorization GCF LCM Radicals Exponential expressions Uniform Motion Problems Ratio Proportions Direct variation Inverse variation
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 Factorial Variations without repetition Variations with repetition Permutations with repetition Permutations without repetition Exercises Circular permutations Binomial coefficient Combinations with repetition Combinations without repetition
 Arithmetic mean

 Combinatorics Variations without repetition Take a set A of n different elements. Choose m elements in a specific order. Each such choice is called a variation of n elements choose m. How many variations are there? The number of variations is given by the formula: Vn,m=n(n-1)(n-2).....(n-m+1), or what is equivalent: Let's see the following example: If we have a set {0, 1, 2, 3}, then the variations of size 2 are all the permutations of subsets of size 2. The subsets are the following: {0, 1} {0, 2} {0, 3} {1, 2} {1, 3} {2, 3} {1, 0} {2, 0} {3, 0} {2, 1} {3, 1} {3, 2} There are 12 total variations on the set. Using the formula: Enter the number of elements of the set A and choose a number m (m n = m = Vn,m=