Principle Of Counting

By Author: Pierce Brosnan
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Introduction to counting principles:

All branches of mathematics are having their own fundamental theorems. Fundamental theorems are considered as an important base in following the rest of the materials. Let us consider some of the fundamental theorems or principles that are used. They are of three types of counting principles as follows,

Fundamental theorem of arithmetic
Fundamental theorem of algebra
Fundamental theorem of linear programming.

Fundamental Counting Principles:

In fundamentals of arithmetic every integer that are greater than one, either prime or composite can be expressed as an only one of its kind product of prime numbers.

In fundamentals of algebra every polynomial which have degree greater than 0 must produce the result as one real or complex number.

In fundamentals of linear programming the result occur at single corner point or between two corner points of a line segment, if only linear programming problems are having any solutions.

Sample Spaces:

Sample space refers to A when it is capable of listing all the possible ...
... outcomes. ‘S’ is the notation of sample space.

Consider the experiments of flipping a coin along with the experiment of rolling of a die. The sample spaces which are possible for both of these experiments are taken as S = { H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}. There are twelve possible ways of outcomes. The fundamental counting principles shows us that there are twelve possible ways not needed to list them as all.

Permutations

Arrangement of objects, without any duplications are called permutations. Permutations is also a type of couting principles. Important consideration is order in permutations. These are the two important considerations in permutations. Another possible way for defining the permutation is the possible number of arrangements.

P(n,r) = n!/(n-r)!

Permutations will always be a whole number since it is the possible arrangements or counting of numbers. Always equal division of numerator will be given by the denominator.

The variable n refers to the value of total number of objects. The r is the number of actually choosed objects.

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