# Probability 1: Combinatorial Analysis

 .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } Define combinatorial analysis (or combinatorics) Combinatorics is a branch of mathematics that studies countable discrete structures. It includes studying counting, ordering and other problems. The basic principle of counting If event A has m possible outcomes, and event B has n possible outcomes, then there are m*n possible outcomes of the two experiments together. Number of permutations of n objects n*(n-1)*(n-2)*...*3*2*1 = n! Number of permutations of n objects, of which n1 are alike, n2 are alike, ... nr are alike. The number of distinct subsets of size k that can be selected from a set of n objects (order of objects is irrelevant) , a.k.a. the binomial coefficient. The number of distinct ordered subsets of size k that can be selected from a set of n objects (order of objects is relevant) Pascal's Rule (a combinatorial identity about binomial coefficients) , for 1 ≤ r ≤ n The binomial theorem Binomial theorem describes the algebraic expansion of powers of a binomial. The number of subsets of a set of n elements 2n   (this includes the null subset) The number of possible partitions of a set of n objects into r distinct groups (order irrelevant)  , a.k.a. the multinomial coefficient The multinomial theorem  (the sum is over all non-negative integers n1, n2, ..., nr such that n1+n2+...+nr = n) The number of distinct positive integer-valued vectors  satisfying  The number of distinct non-negative integer-valued vectors  satisfying  Type I error A false positiveThe null hypothesis is rejected when it is actually true."I falsely think that the Alternative hypothesis is true." Type II error A false negativeThe null hypothesis is accepted when it is actually false."I falsely think that the Alternative hypothesis is false." .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } Authorbarium ID220740 Card SetProbability 1: Combinatorial Analysis DescriptionCombinatorial analysis formulas and definitions used in probability theory Updated2013-05-29T01:07:15Z Show Answers