Permutation and Combination is an important topic in mathematics and quantitative aptitude. It is useful for school exams, competitive exams, banking, SSC, railway, entrance tests and campus placement exams. The topic checks how clearly a student can count, compare and interpret information.
This lesson explains permutation and combination in easy language. It includes definitions, formulas, shortcut ideas, solved examples, practice questions, answers and FAQs. The writing is kept simple so beginners can learn step by step.
What Is Permutation and Combination?
Permutation and combination are counting methods. Permutation is used when order matters. Combination is used when order does not matter.
Important Terms
| Point | Details |
|---|---|
| Factorial | Product of natural numbers up to a number |
| Permutation | Arrangement where order matters |
| Combination | Selection where order does not matter |
| nPr | Number of arrangements of r objects from n |
| nCr | Number of selections of r objects from n |
Important Formulas and Rules
| Point | Details |
|---|---|
| Factorial | n! = n x (n-1) x … x 1 |
| Permutation | nPr = n! / (n-r)! |
| Combination | nCr = n! / r!(n-r)! |
| Relation | nPr = nCr x r! |
| Symmetry | nCr = nC(n-r) |
Step-by-Step Method
- Decide whether order matters.
- If order matters, use permutation.
- If order does not matter, use combination.
- Check whether repetition is allowed.
- Substitute values and simplify factorials.
Shortcut Tricks
- Arrangement means permutation.
- Selection means combination.
- Committee questions usually use combination.
- Rank, word arrangement and seating use permutation.
- nC0 and nCn are always 1.
Common Question Types
| Point | Details |
|---|---|
| Arrangement | Use nPr |
| Selection | Use nCr |
| Word arrangement | Use factorials |
| Committee | Use combinations |
| Digit numbers | Check repetition condition |
Solved Examples
Example 1
Find 5P2.
5P2 = 5!/(5-2)! = 5 x 4 = 20.
Example 2
Find 5C2.
5C2 = 5!/(2!3!) = 10.
Example 3
Arrange letters A, B, C.
3! = 6 ways.
Example 4
Select 2 students from 5.
5C2 = 10 ways.
Example 5
How many ways to arrange 4 books?
4! = 24 ways.
Exam Style Examples
Question 1
How many 3-letter arrangements can be made from 5 different letters?
Order matters, so use 5P3 = 5 x 4 x 3 = 60.
Letter arrangement is permutation.
Question 2
A team of 3 is selected from 8 students. Find number of teams.
Order does not matter, so use 8C3 = 56.
Selection is combination.
Question 3
How many ways can the letters of the word LEVEL be arranged?
Total letters = 5. L repeats 2 times and E repeats 2 times. Arrangements = 5!/(2!2!) = 30.
Repeated letters divide the factorial.
Common Mistakes
- Using permutation when order does not matter.
- Using combination for arrangement questions.
- Forgetting repeated letters.
- Not simplifying factorials.
- Ignoring repetition condition in digit questions.
Practice Questions
- Find 6P2.
- Find 6C2.
- Arrange 5 people in a row.
- Select 3 from 7.
- Find 4!.
- Find 7C0.
- How many 2 digit numbers from 1,2,3 without repetition?
- Arrange letters of BALL.
- Find 5P3.
- Find 8C2.
Answers to Practice Questions
- 30
- 15
- 120
- 35
- 24
- 1
- 6
- 12
- 60
- 28
Frequently Asked Questions
What is permutation?
Permutation is arrangement where order matters.
What is combination?
Combination is selection where order does not matter.
What is factorial?
Factorial is product of positive integers up to that number.
When should I use nPr?
Use nPr when arranging objects.
When should I use nCr?
Use nCr when selecting objects.
Revision Notes
Permutation means arrangement and combination means selection. The first decision is whether order matters.
For revision, do not only read formulas. Solve examples and explain why each formula is used. This makes the concept stronger.
Conclusion
Permutation and combination become easy when you identify order and selection correctly.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.
Additional Exam Practice Note
Permutation and Combination questions reward clear thinking. First identify what is being counted or compared. Then decide whether order matters, whether repetition is allowed, whether a table or chart must be interpreted, and whether the final answer should be a number, ratio, percentage or conclusion.
In exams, avoid doing all calculations mentally. Write the key values in a small table or equation. This prevents errors in long questions and makes it easier to verify the final answer.
After solving, check the range of the answer. Number of ways cannot be negative. A percentage comparison should match the direction of increase or decrease. These small checks improve accuracy.