On matchings, derangements, and rencontres

• Main Authors: Angelico, Joyce T., De la Cruz, Elaine C.
• Format: text
• Language: English
• Published: Animo Repository 1995
• Subjects: Matching theory; Combinatorial analysis; Problem solving
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16239
• Institution: De La Salle University

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.