Maths Extension 1 Year 11 - Module 4 - Lesson 6

Combinations ($^nC_r$)

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name
Date
Class

1. Lesson focus

Combinations nCr. An unordered selection of r objects from n distinct objects has nCr=n!/[r!(n−r)!]; order does not matter.

Success criteria

  • Apply the lesson method accurately in a routine example.
  • Show each algebraic or domain step and check the result.
  • Explain why the method and restrictions fit the question.

2. Worked practice

1. Evaluate 10C3.

2. How many pairs can be selected from 12 students?

3. A team of 4 is chosen from 8 students. How many teams?

3. Challenge

A committee has at least 2 women chosen from 6 women and 4 men; it has 3 members. How many committees?

4. Multiple choice

How many ways can a 3-person committee be selected from 8 people?

A. 8C3=56

B. 8P3=336

C. 3!=6

D. 8×3=24

Worked answer key

Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.

1. Evaluate 10C3.

10C3=(10×9×8)/(3×2×1)=120.

2. How many pairs can be selected from 12 students?

12C2=12×11/2=66.

3. A team of 4 is chosen from 8 students. How many teams?

8C4=8×7×6×5/(4×3×2×1)=70.

Challenge. A committee has at least 2 women chosen from 6 women and 4 men; it has 3 members. How many committees?

Exactly 2 women: 6C2×4C1=15×4=60. Exactly 3 women: 6C3=20. Total 80.

Multiple choice. How many ways can a 3-person committee be selected from 8 people?

Correct answer: A. A committee is unordered, so use combinations: 8C3=8×7×6/(3×2×1)=56.

HSCScience - Printable lesson worksheet - Maths Extension 1 Year 11 - Module 4 - Lesson 6

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