Discreet Mathematics

Hello, today we are going to discuss the discreet mathematics. Discreete mathematics is concerned with the study of distinct objects. Discreet mathematics provides the mathematical foundation for many courses in the field of Computer science, Operation research, Chemistry, Biology and other branches of Engineering. It involves the study of topics like Languages and logics, proof methods, graph theory, sets, relations and functions and permutations and combinations.

Let us have a look at some important terms of Discreet Mathematics.

MATRICES: A matrix is a rectangular arrangement of 'k' number of things. The entries in the rectangular arrangement (arrangement in rows and column) are enclosed in square brackets for example [a b c].
DETERMINANTS: For every square matrix there exists determinants which have the same elements as the matrix.The determinants of a square matrix, A= [a_ij]t can be written as |A|.
PERMUTATIONS: Permutations refer to the different arrangements of a number of things; Permutation is helpful to find the number of ways of doing a job. Number of ways or arrangements of n things taken r  things at a time can be found in this way:
       ⁿP_r= n!/(n-r)! Where n! = n. (n-1). (n-2)…………..3.2.1 
COMBINATIONS: Combination refers to the ways of selection of some or all of the objects from a group of objects, different groups of members, teams of players and effective selection of objects from n distinct objects can be easily calculated by using theory of combinations.
                                                    Solving discreet problems:
For practice purpose, here are few solved examples on permutations and combinations:

 Problem no.1: In how many ways can three prizes be distributed among 4 boys if

·         No one gets more than one prize.

·          A boy can get any number of prizes. 

Solution. there are total three prizes the first prize can be distributed in 4 ways and second and third prize can be distributed in 3 and 2 ways respectively as a boy can have only one prize so the total number of ways = 4.3.2= 24
 but when a buy can have any number of prizes every prize can be distributed in all 4 ways so total number of ways in this case are =4.4.4=64
Problem no.2. Given five different green dyes, four different blue dyes and three different red dyes how many combinations can be formed by selecting at least one green and one blue dye?
Solution. Number of ways of selecting at least one green dye
 =31
Now out of four blue dyes we can select  in
= 15, now after selecting one green and one blue dye we can select one or no red dye in
= 8, now the total no of ways = (31)(15)(8)= 372
In such a manner one can solve the various discreet mathematics problems .