Permutations and Combinations — Class 11 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Permutations and Combinations" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Permutations and Combinations" — 8 important questions with detailed answers for C…
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Key Questions Covered:
- Find the value of 8P3 and 8C3.
- In how many ways can 5 people be arranged in a row?
- A committee of 4 people is to be selected from a group of 10 people. In how m…
- + 5 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Find the value of 8P3 and 8C3. | ✓ Solved |
| In how many ways can 5 people be arranged in a row? | ✓ Solved |
| A committee of 4 people is to be selected from a group of… | ✓ Solved |
Showing 3 of 8 questions
Q1: Find the value of 8P3 and 8C3.
Step 1: Recall the permutation formula.
nPr = n! / (n - r)!
Step 2: Calculate 8P3.
8P3 = 8! / (8 - 3)!
= 8! / 5!
= (8 × 7 × 6 × 5!) / 5!
= 8 × 7 × 6
= 56 × 6
= 336
Step 3: Recall the combination formula.
nCr = n! / [r!(n - r)!]
Step 4: Calculate 8C3.
8C3 = 8! / [3!(8 - 3)!]
= 8! / (3! × 5!)
= (8 ...
Q2: In how many ways can 5 people be arranged in a row?
Step 1: Understand the problem.
We need to arrange 5 distinct people in 5 positions.
This is a permutation problem where order matters.
Step 2: Apply the permutation formula.
nPn = n! (all n objects arranged in all n positions)
Step 3: Calculate 5P5 = 5!
5! = 5 × 4 × 3 × 2 × 1
Step 4: Compute ste...
Q3: A committee of 4 people is to be selected from a group of 10 people. In how many ways can this be done?
Step 1: Understand the problem.
We need to select 4 people from 10.
Order does not matter (a committee {A, B, C, D} is the same as {B, A, D, C}).
This is a combination problem.
Step 2: Apply the combination formula.
10C4 = 10! / [4!(10 - 4)!]
= 10! / (4! × 6!)
Step 3: Simplify.
10C4 = (10 × 9 × 8 ...
Showing 3 of 8 questions. Visit the full page for complete solutions.