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5.Permutations – Fundamental Counting
Class 11 • Mathematics • NCERT
Permutations – Fundamental Counting
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This lesson introduces the Fundamental Principle of Counting and the basic idea of permutations as per NCERT Class 11. Students learn how to count outcomes systematically using simple rules and factorial notation.
Lesson Objectives
- Understand the need for counting techniques.
- Learn the Fundamental Principle of Counting.
- Use addition and multiplication rules.
- Understand factorial notation.
1. Need for Counting
In many situations, we need to find the number of possible outcomes without listing them.
Example:
How many ways can we choose clothes, seats, passwords, or arrangements?
How many ways can we choose clothes, seats, passwords, or arrangements?
2. Fundamental Principle of Counting
If an operation can be performed in m ways and another independent operation in n ways, then both operations together can be performed in m × n ways.
This is called the Multiplication Rule.
3. Addition Rule of Counting
If a task can be done in m ways or in n ways (but not both), then the task can be done in m + n ways.
Example:
Choosing a pen or a pencil from separate groups.
Choosing a pen or a pencil from separate groups.
4. Factorial Notation
The product of the first n natural numbers is called factorial of n.
n! = n × (n − 1) × (n − 2) × … × 1
0! = 1
0! = 1
5. Simple NCERT Examples
• If there are 3 shirts and 2 trousers, total outfits = 3 × 2 = 6
• 4! = 4 × 3 × 2 × 1 = 24
• 4! = 4 × 3 × 2 × 1 = 24
Practice Questions (NCERT)
- State the Fundamental Principle of Counting.
- When do we use the addition rule?
- When do we use the multiplication rule?
- Find the value of 5!.
- What is the value of 0!?
- If there are 4 choices of food and 3 choices of drink, how many combinations?
- How many ways can a task be done if it can be done in 2 or 5 ways?
- Is factorial defined for negative numbers?
- Why are counting techniques important?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- If one operation can be done in m ways and another in n ways, then together in m × n ways.
- When tasks are mutually exclusive.
- When tasks are performed together.
- 120
- 1
- 12
- 7
- No
- To count outcomes efficiently.
- Yes
© Aviate Learning – Permutations & Combinations (NCERT Class 11)