Fundamental Theorems & counting principles

May 19th, 2015
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Arithmetic : Every integer greater than one is either prime or can be expressed as an unique product of prime numbers Algebra : Every polynomial function on one variable of degree n > 0 has at least one real or complex zero

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Stats: Counting TechniquesFundamental TheoremsArithmeticEvery integer greater than one is either prime or can be expressed as an unique product of prime numbers AlgebraEvery polynomial function on one variable of degree n > 0 has at least one real or complex zero. Linear ProgrammingIf there is a solution to a linear programming problem, then it will occur at a corner point or on a boundary between two or more corner points Fundamental Counting PrincipleIn a sequence of events, the total possible number of ways all events can performed is the product of the possible number of ways each individual event can be performed. The Bluman text calls this multiplication principle 2. FactorialsIf n is a positive integer, then n! = n (n-1) (n-2) ... (3)(2)(1) n! = n (n-1)!A special case is 0! 0! = 1PermutationsA permutation is an arrangement of objects without repetition where order is important. Permutations using all the objectsA permutation of n objects, arranged into one group of size n, without repetition, and order being important is: nPn = P(n,n) = n!Example: Find all permutations of the letters "ABC" ABC ACB BAC BCA CAB CBAPermutations of some of the objectsA permutation of n objects, arranged in groups of size r, without repetition, and order being important is: nPr = P(n,r) = n! / (n-r)!Example: Find all two-letter permutations of the letters "ABC" AB AC BA BC CA CBShortcut formula for finding a permutationAssuming

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