Maths Extension 1 Year 11 - Module 4 - Lesson 3

Permutations ($^nP_r$)

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

Permutations nPr. An ordered selection of r objects from n distinct objects has nPr=n!/(n−r)! outcomes.

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 8P3.

2. How many ways can gold and silver be awarded among 9 finalists?

3. A 4-character code uses distinct symbols chosen from 10. How many codes?

3. Challenge

How many ways can 1st, 2nd and 3rd place be assigned to 7 runners?

4. Multiple choice

Evaluate 7P2.

A. 21

B. 42

C. 14

D. 49

Worked answer key

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

1. Evaluate 8P3.

8P3=8×7×6=336.

2. How many ways can gold and silver be awarded among 9 finalists?

Order matters: 9P2=9×8=72.

3. A 4-character code uses distinct symbols chosen from 10. How many codes?

10P4=10×9×8×7=5040.

Challenge. How many ways can 1st, 2nd and 3rd place be assigned to 7 runners?

7P3=7×6×5=210.

Multiple choice. Evaluate 7P2.

Correct answer: B. 7P2=7×6 because the first choice leaves six options for the second.

HSCScience - Printable lesson worksheet - Maths Extension 1 Year 11 - Module 4 - Lesson 3

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