Combination

Grade 9 · Mathematics

Semester 2 | Period 6 | Week 35

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Subject: Mathematics

Semester: 2

Period: 6

Week: 35

WEEK 35

Class: Grade 9
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Combination
Focus: Arrangements Without Regard to Order

SPECIFIC OBJECTIVES:

By the end of the lesson, pupils should be able to:

  1. Differentiate between permutation and combination.
  2. Explain that in combinations, order does not matter.
  3. Use the combination formula nCr= n!      to solve problems.

                                                         r!(n−r)!  

  1. Solve real-life problems such as forming committees or choosing teams.
  2. Apply combinations in probability and decision-making scenarios.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Group exercises
  • Class discussions
  • Real-life problem-solving

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and marker
  • Flashcards with letters or numbers
  • Worksheets with combination problems
  • Calculator (optional)

 

PERIOD 1 & 2: Introduction and Formula

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Anticipation (Warm-up)

Teacher asks: “If you have 5 students, how many ways can you select 2 to form a committee?”

Pupils suggest answers; teacher links to combination concept.

Step 2 – Building Knowledge (Explanation)

Explains difference between permutation (order matters) and combination (order does not matter).

Pupils take notes and ask questions.

Step 3 – Formula Introduction

Writes formula nCr=  n!

                               r!(n−r)!

Explains n = total items, r = items chosen.

Pupils copy formula and take notes.

Step 4 – Demonstration

Example: Select 2 students from 4: 4C2=4!

                                                           2!2!

                                                            =6

Lists all combinations.

Pupils observe and write down results.

NOTE ON BOARD:

  • Permutation: order matters
  • Combination: order does not matter
  • Combination formula: nCr=   n!

       r!(n−r)!

EVALUATION (5 exercises):

  1. Find 5C2.
  2. Calculate 6C3.
  3. Choose 3 books from 5. How many ways?
  4. 7C1 = ?
  5. 8C2 = ?

CLASSWORK (5 questions):

  1. 4C2 = ?
  2. Choose 2 students from 6. Find number of ways.
  3. 5C3 = ?
  4. Form a team of 3 from 7 students. Calculate combinations.
  5. 9C2 = ?

ASSIGNMENT (5 tasks):

  1. Find 6C2.
  2. A committee of 3 from 8 people. Calculate number of combinations.
  3. Choose 4 books from 6. Find total ways.
  4. 10C3 = ?
  5. Create a real-life problem involving combination and solve it.

 

PERIOD 3 & 4: Practical Examples and Applications

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Anticipation

Teacher presents scenario: forming a 3-person team from 5 students.

Pupils suggest methods.

Step 2 – Building Knowledge

Explains that for team selection or committee formation, order does not matter, so combination is used.

Pupils listen and take notes.

Step 3 – Demonstration

Example: 5 students A, B, C, D, E. Select 3 for a committee: 5C3=10. Lists all combinations.

Pupils list combinations and verify.

Step 4 – Guided Practice

More examples:

  
  • Choosing 2 players from 6 for a team
  • Selecting 3 books from 5 to read
  • Forming 4-person committees from 7 students | Pupils solve examples with guidance.

EVALUATION (5 exercises):

  1. Find 7C2.
  2. Choose 3 students from 6. How many ways?
  3. 5C4 = ?
  4. Selecting 2 fruits from 5 types. Calculate combinations.
  5. 8C3 = ?

CLASSWORK (5 questions):

  1. 6C2 = ?
  2. Choose 3 books from 7. Find combinations.
  3. Form a 4-person team from 6. Calculate number of ways.
  4. 9C2 = ?
  5. Select 2 students from 5 for roles. How many ways?

ASSIGNMENT (5 tasks):

  1. 10C2 = ?
  2. Form a 3-member committee from 8 students. Calculate number of ways.
  3. Choose 4 books from 6. Find total ways.
  4. Create a real-life problem using combination and solve.
  5. 12C3 = ?

 

PERIOD 5: Application of Permutation and Combination in Probability

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Anticipation

Teacher asks: “If you randomly pick 3 cards from a deck, how many ways can this happen?”

Pupils suggest methods; teacher links to combination.

Step 2 – Building Knowledge

Shows how permutations and combinations are applied in probability: P(event) = favorable outcomes / total outcomes.

Pupils copy and take notes.

Step 3 – Demonstration

Example: 5 students, choose 2 for president & vice president (permutation) vs choose 2 for a committee (combination).

Pupils differentiate between permutation and combination scenarios.

Step 4 – Guided Practice

More probability examples involving selection of items, numbers, or positions.

Pupils solve examples with guidance.

EVALUATION (5 exercises):

  1. Probability of choosing 2 students from 5 to form a committee.
  2. Find 4C2 and explain why combination is used.
  3. 3 students chosen from 6 to form a team. Probability example.
  4. Compare 3P2 and 3C2 for same group of students.
  5. Application: Selecting books for a library shelf.

CLASSWORK (5 questions):

  1. 5C3 = ?
  2. 6C2 = ?
  3. Probability of selecting 2 red balls from 5 balls (3 red, 2 blue).
  4. 4P2 = ? vs 4C2 = ? Explain.
  5. Form 2-person committees from 6 students. Number of ways?

ASSIGNMENT (5 tasks):

  1. 7C3 = ?
  2. Difference between 5P2 and 5C2 in real-life context.
  3. Form a team of 3 from 8 students. Calculate combinations.
  4. Create a probability question using combination and solve.
  5. Explain a scenario where permutation is used instead of combination.