Stats: Counting Techniques Fundamental Theorems 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. Linear Programming If 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 Principle In 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. Factorials If 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! = 1 Permutations A permutation is an arrangement of objects without repetition where order is important. Permutations using all the objects A 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" ABCACBBACBCACABCBA Permutations of some of the objects A permutation of n objects, arranged in groups of size r, without repetition, and order being
