Fundamental Principle of Counting





The page fundamental principle of counting is going to explain the definition and example problems.This is the basic concept of understanding the topic permutation and combination.There are two kinds of rules in the topic fundamental principle of counting.

(i) Fundamental principle of multiplication

(ii) Fundamental principle of addition

Definition of multiplication rules

If there are two jobs such that one of the job can be completed in ā€œPā€ ways and when it has been completed in any one these m ways, second job can be completed in ā€œQā€ ways, then the two jobs in succession can be completed in P x Q ways.

To understand this definition, let us consider the following situation For example, in a class there are 2 boys and 3 girls. The teacher wants to select a boy and a girl in a class function. In how many ways can the teacher makes this selection?

   Name of boy in the class           Name of girls in the class

                Kevin                                 July

                Karim                                 Angola

                                                        Cristina                 

She can select a girl or a boy in the following ways

(Kevin, July), (Kevin, Angola), (Kevin, Cristina), (Karim, July), (Karim, Angola), (Karim, Cristina)

She has 6 ways to make this selection. Since there are 2 boys and 3 girls we can make this set which is containing a boy and a girl easily. For example, if there are 15 boys and 30 girls, this process will be more difficult. To avoid this kind of difficulties we are going to apply the topic fundamental principle of multiplication.

How to decide in which type of question we have to apply the multiplication rule:

First, we have to analyze whether we have to do both jobs or we can just do only one job. If we have to do both jobs we have to apply this multiplication rule.

Definition of addition rules

If there are two jobs such that they can be performed independently in "P ways and "Q" ways respectively,then either of the jobs can be performed in (P + Q) ways.

To understand this definition, let us consider the following situation For example, in a class there are 2 boys and 3 girls. The teacher wants to select a boy and a girl in a class function. In how many ways can the teacher makes this selection?

   Name of boy in the class           Name of girls in the class

                Kevin                                 July

                Karim                                 Angola

                                                        Cristina                 

Here each boy has a chance of getting selected.

(Kevin, Karim, July, Angola, Cristina)