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6.Combinations & Applications
Class 11 • Mathematics • NCERT
Combinations & Applications
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This lesson introduces combinations and their applications as per NCERT Class 11. Students learn how to select objects without considering order and apply the combination formula to simple, exam-oriented problems.
Lesson Objectives
- Understand the concept of combinations.
- Differentiate between permutations and combinations.
- Learn the formula for combinations.
- Apply combinations to simple problems.
1. What Is a Combination?
A combination is a selection of objects in which the order does not matter.
Example:
Selecting 2 students from a group of 5 students.
Selecting 2 students from a group of 5 students.
2. Combination Formula
The number of ways of selecting r objects from n distinct objects is given by:
nCr = n! / [r!(n − r)!]
3. Difference Between Permutation and Combination
The key difference lies in whether order matters.
• Permutation: Order matters
• Combination: Order does not matter
• Combination: Order does not matter
4. Important Properties (NCERT)
• nC0 = nCn = 1
• nCr = nC(n − r)
• nCr = nPr / r!
• nCr = nC(n − r)
• nCr = nPr / r!
5. Simple NCERT Applications
• Number of ways to choose 2 books from 5 books = 5C2 = 10
• Number of ways to select a committee of 3 from 7 people = 7C3
• Number of ways to select a committee of 3 from 7 people = 7C3
Practice Questions (NCERT)
- Define a combination.
- Write the formula for nCr.
- What is the value of 6C0?
- Find the value of 5C2.
- State one difference between permutation and combination.
- Write the value of nC1.
- Find 7C3.
- Is order important in combinations?
- Write one application of combinations.
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- Selection of objects where order does not matter.
- n! / [r!(n − r)!]
- 1
- 10
- Order matters in permutation but not in combination.
- n
- 35
- No
- Forming committees.
- Yes
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