On matchings, derangements, and rencontres
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 w...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | text |
| Language: | English |
| Published: |
Animo Repository
1995
|
| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/16239 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | De La Salle University |
| Language: | English |
| 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. |
|---|