NCERT Books for Class 11 Maths Chapter 7 - Permutations and Combinations - Free PDF Download
FAQs on NCERT Books Free Download for Class 11 Maths Chapter 7 - Permutations and Combinations
1. What are the most frequently asked types of questions from Chapter 7, Permutations and Combinations, in the Class 11 exams?
Based on previous board exam trends for the CBSE 2025-26 session, the most important question types from this chapter involve:
Finding the number of arrangements of letters in a word (with or without repeated letters).
Forming numbers (e.g., 3-digit or 4-digit numbers) with given digits under specific constraints (e.g., even numbers, divisible by 5).
Problems involving selecting a committee or team from a group of people with certain conditions.
Arrangement problems where certain items must always be together or never be together.
2. Which topics in Permutations and Combinations are most important for scoring high marks?
To score high marks, students should focus on:
The Fundamental Principle of Counting: This is the base for the entire chapter and is often tested in 1 or 2-mark questions.
Distinguishing between Permutation and Combination: Understanding when order matters (permutation) and when it does not (combination) is crucial for solving most problems correctly.
Permutations with restrictions: Questions where objects are repeated (like in the word 'INDEPENDENCE') or have fixed positions are very common.
Combinations with specific conditions: Problems like selecting a team with at least one girl or at most two boys are considered high-value.
3. What kind of 5-mark or long-answer questions can be expected from Permutations and Combinations?
For the Class 11 final exams, a 5-mark question from this chapter is typically a multi-step or complex problem. Expect questions that may require using both permutation and combination concepts, or problems with multiple constraints. For example, a question might ask you to first select a specific number of vowels and consonants from a word and then arrange them to form new words. These are often classified as HOTS (Higher Order Thinking Skills) questions.
4. What is the most common mistake students make when deciding whether to use a permutation or a combination?
The most common conceptual error is confusing selection with arrangement. Students should remember this simple rule: if the order of the chosen items matters, it is a permutation (like arranging people for a photo). If the order does not matter, it is a combination (like choosing a team of 5 players). Misinterpreting this fundamental difference is the primary reason for incorrect answers in exams.
5. How are questions on the 'Fundamental Principle of Counting' different from direct formula-based questions?
The Fundamental Principle of Counting is the underlying logic for solving arrangement problems by breaking them into sequential stages and multiplying the number of choices at each stage. It is used when a direct formula for permutation or combination doesn't fit neatly. In exams, questions based purely on this principle are often shorter (1-2 marks), whereas problems requiring direct application of the nPr or nCr formulas tend to carry more weight (3-5 marks).
6. For questions involving arrangements with repeated letters (e.g., 'MISSISSIPPI'), what is the underlying logic for dividing by the factorials of the repeated items?
This is a crucial concept for scoring well on arrangement problems. The logic is to correct for overcounting. First, we calculate the total arrangements as if all letters were distinct (n!). However, since some letters are identical, swapping their positions doesn't create a new, unique arrangement. We divide by the factorial of the count of each repeated letter (e.g., 4! for the four 'I's in 'MISSISSIPPI') to remove these identical, non-distinguishable permutations from the total count.
7. How can I structure my answer for a permutation or combination problem to secure full marks?
To ensure you get full marks as per the CBSE evaluation guidelines, follow these steps:
Step 1: Identify and state whether the problem requires a permutation or combination, and briefly justify why (e.g., "Since the order of selection does not matter, we will use combination").
Step 2: Write the relevant formula, such as nCr = n! / (r! * (n-r)!).
Step 3: Clearly substitute the values of 'n' and 'r' from the question into the formula.
Step 4: Show the key calculation steps rather than just writing the final answer.
Step 5: Conclude with a clear, final statement that answers the original question.
8. Are there any important questions that combine concepts from both permutations and combinations?
Yes, these are considered important, high-value questions. A classic example is a problem where you must first select a group from a larger pool (a combination) and then arrange the selected members (a permutation). For instance: "From a group of 7 men and 4 women, how many ways can a committee of 5 be formed and then arranged in a row if the committee must have exactly 3 men?" Solving this requires both the combination formula for selection and the permutation formula for arrangement.
