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# Fundamental Principle Of Counting - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• 106 Questions around this concept.

## Solve by difficulty

How many different three-letter codes can be formed using the letters A, B, C, D, E, F, G, and H if repetition is allowed and first letter is A?

How many different three-letter codes can be formed using the letters A, B, C, D, E, F, G, and H if repetition is allowed and the first letter is E?

How many different four-letter codes can be formed using the letters A, B, C, D, and E if repetition is allowed and the codes should have the starting letter D?

If the digits 1, 2, 3, 4, and 5 are arranged to form a five-digit number, how many different numbers can be created by swapping the positions of any two digits?

In a restaurant, there are 6 different flavours of ice cream and 4 different types of toppings. How many different ice cream sundaes can be created if one flavour of ice cream and one topping are chosen?

In a race, there are 8 participants. In how many ways can the gold, silver, and bronze medals be awarded if the previous year's winner cannot win the gold medal again?

## Concepts Covered - 1

FUNDAMENTAL PRINCIPLE OF COUNTING

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)

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.

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))

## Study it with Videos

FUNDAMENTAL PRINCIPLE OF COUNTING

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