Fundamental Principle Of Counting - Practice Questions & MCQ

Fundamental principle of counting is a rule used to find the total number of outcomes possible in a given situation. Fundamental principle of counting can be classified into two types 

1. Multiplication Rule (AND rule)
2. Addition Rule (OR rule)

Multiplication Rule

If a certain work W can be completed by doing 2 tasks, first doing task A AND then doing task B.  A can be done in m ways and following that B can be done in n ways, then the number of ways of doing the work W is (m x n) ways. 

For example, let's say a person wants to travel from Noida to Gurgaon, and he has to travel via New Delhi. It is given that the person can travel from Noida to New Delhi in 3 different ways and from New Delhi to Gurgaon in 5 different ways.

So, in this case, to complete his work (reach Gurgaon) he has to do two tasks one after the other, first traveling from Noida to New Delhi (task A) and then from New Delhi to Gurgaon (task B), as he has 3 different ways of reaching New Delhi (doing task A), and he has 5 different ways to reach Gurgaon from New Delhi (doing task B), so in that way, he has a total of 3×5 = 15 different ways to reach Gurgaon from Noida.

Addition Rule

If work W can be completed by doing task A OR task B, and A can be done in m ways and B can be done in n ways (and both cannot occur simultaneously: in this case we call tasks A and B as mutually exclusive), then work W can be done in (m + n) ways.

For example, let’s say that a person can travel from New Delhi to Noida in 3 different types of buses, and 2 different types of trains, so, he can complete the work of going from New Delhi to Noida in 3 + 2 = 5 ways (As work can be completed by going by bus (A) OR by going by train (B))