Master Permutations And Combinations Class 11 Questions And Answers for Higher Marks
FAQs on NCERT Solutions for Class 11 Maths Chapter 6 Permutations And Combinations
1. How do you calculate the factorial of a number (n!)?
Multiply the integer by every positive integer below it down to 1. For example, 5! equals 5 × 4 × 3 × 2 × 1 = 120. Remember the special case: by definition, 0! = 1. To check your work, ensure your product includes all integers from n down to 1.
2. When should you use the Fundamental Principle of Multiplication?
Use this principle to find the total number of outcomes when multiple independent events occur in sequence. If a first event has 'm' possible outcomes and a second has 'n' outcomes, the total number of ways for both to occur is m × n. Simply multiply the options for each step.
3. How can you download the permutations and combinations Class 11 NCERT PDF?
Find the download button for the Class 11 Maths Chapter 6 solutions on this page. Click the link to save the Free PDF to your device. This allows you to study the permutations and combinations class 11 ncert solutions offline, which is great for revision without an internet connection.
4. What is the method for finding permutations when some objects are identical?
First, calculate the factorial of the total number of objects (n!). Then, divide this result by the product of the factorials of the counts for each type of identical object (p₁!, p₂!, etc.). The formula is n! / (p₁! * p₂! * ...), which corrects for overcounting repeated items.
5. How can you use NCERT solutions to quickly check your answers?
Solve a question from your NCERT textbook exercise on your own first. Then, open the solutions and compare your final answer and key formula application. This method helps you instantly spot errors in your logic or calculation without simply copying the provided steps.
6. How do you solve a permutation problem where the order of arrangement matters?
Instruction: Use the permutation formula, P(n, r) = n! / (n-r)!, to find the number of ways to arrange 'r' objects selected from a set of 'n' distinct objects.
Why it matters: This formula is essential when the sequence or position of items is important. Common examples include arranging letters in a word, assigning specific job roles, or determining prize winners.
Steps:
- Identify the total number of distinct objects available, which is 'n'.
- Determine the number of objects you need to arrange, which is 'r'.
- Substitute 'n' and 'r' into the permutation formula.
- Calculate the factorials and simplify the expression to find the answer.
Check: Ensure that n ≥ r. The result must always be a positive integer. A common mistake is using this formula for selection problems where order does not matter (which requires combinations).
Solving permutation problems involves identifying n and r, applying the P(n, r) formula, and simplifying the factorials.
7. How can the Class 11 Maths Chapter 6 NCERT Solutions be used for self-assessment?
Instruction: Our NCERT Solutions for Class 11 Maths Chapter 6 provide a reliable way to gauge your understanding by comparing your independent work against expert-verified methods.
Why it matters: Self-assessment helps you pinpoint weak areas before exams. It shifts you from passive learning to active problem-solving, which is crucial for building confidence and improving your scores.
Steps:
- Attempt a full exercise from the NCERT textbook without any help.
- After finishing, open the Vedantu solutions page for that specific exercise.
- Compare your final answers first. If an answer is incorrect, review the step-by-step logic.
- Note down any conceptual errors, like using permutation instead of combination.
Tip: Do not just look at the final answer. Focus on understanding the method and the formulas used in each step, as this is where marks are often awarded in exams.
8. What is the method for solving combination problems where selection order is irrelevant?
Instruction: Apply the combination formula, C(n, r) = n! / [r!(n-r)!], to calculate the number of ways to choose 'r' objects from a set of 'n' distinct objects.
Why it matters: This is used for scenarios like selecting a committee from a group of people or choosing a set of books, where the composition of the group is what counts, not the sequence of selection.
Steps:
- Confirm the problem is about selection, not arrangement. Keywords like “choose” or “select” are good indicators.
- Identify the total number of items available (n).
- Determine the number of items to choose (r).
- Substitute these values into the C(n, r) formula and simplify.
Check: The number of combinations C(n, r) will always be less than or equal to the number of permutations P(n, r) for the same n and r, as combinations do not count different orderings.
For combination problems, use the C(n, r) formula when order does not matter, focusing on selection rather than arrangement.
9. How do you decide whether to use permutation or combination for a question?
Instruction: Analyse the problem statement for keywords that imply order is important. If the arrangement matters, use permutation. If only the selection of a group matters, use combination.
Why it matters: Correctly identifying the problem type is the most critical first step. Choosing the wrong formula will lead to a completely incorrect answer for permutations and combinations questions and answers class 11.
Steps:
- Read the question carefully to understand the core task.
- Look for words like "arrange," "order," "rank," or "position." These signal a permutation.
- Look for words like "select," "choose," "group," or "committee." These signal a combination.
- Ask: "Does changing the order of the chosen items create a new outcome?" If yes, it's a permutation. If no, it's a combination.
Example: Arranging 3 people in a line is a permutation. Choosing a team of 3 people is a combination.
10. What is the best way to practise the Miscellaneous Exercise for Permutations and Combinations Class 11?
Instruction: Tackle the Miscellaneous Exercise questions after you have thoroughly completed all the main exercises in the chapter. Use the solutions PDF as a final check, not a guide.
Why it matters: The Miscellaneous Exercise contains more complex problems that mix concepts from the entire chapter. Mastering these is a strong indicator of exam readiness.
Steps:
- Revise all chapter concepts and formulas before starting.
- Attempt each problem on your own, trying to identify the correct approach (P, C, or mixed).
- If you are stuck, refer to the solution to understand only the initial hint.
- After solving, compare your full method with the one in the Free PDF to learn the most efficient way.
Tip: Many of these questions require a combination of the Fundamental Principle of Counting along with permutation or combination formulas. This tests your deeper understanding of the chapter.

















