On matchings, derangements, and rencontres
Date of Publication
1995
Document Type
Bachelor's Thesis
Degree Name
Bachelor of Science in Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Abstract/Summary
This paper discussed how to obtain the solution to the (n,k)-matching problem, which may be started as follows:A matching question on an examination has k questions with n possible answers to choose from, each question having a unique answer. If a student guesses the answers at random, in how many ways can it happen that r correct answers are obtained and what is the probability that it will happen? When n = k and r = 0, the result corresponds to the number of derangements of a given set of n objects. D(n, n, 0), in our terminology, represents the number of rearrangements of n objects where none retain its original position.The classical problems des rencontres viewed derangement problem as a special case. This counts the number of permutations of a set of n object in which r objects retain their rightful places.Several formulas for the (n,k)-matching problems, derangements, and rencontres were proved and applied. These include recursive formulas for D(n, k, r) which gives the number of ways that n correct answers can be obtained in an (n,k)-matching examination.
Abstract Format
html
Language
English
Format
Accession Number
TU07039
Shelf Location
Archives, The Learning Commons, 12F, Henry Sy Sr. Hall
Physical Description
56 leaves
Keywords
Matching theory; Combinatorial analysis; Problem solving
Recommended Citation
Angelico, J. T., & De la Cruz, E. C. (1995). On matchings, derangements, and rencontres. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/16239
