Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Define permutations and their significance.
• Solve real-life problems involving permutations.
• Apply the concept of permutations to arrange objects.
• Analyze data sets to make predictions based on arrangements.

Lesson summary

In Ghana, we see arrangements everywhere. Think about how a market woman arranges different fruits in a row to attract customers, how students are seated for an examination, or how the national football team lines up before a match. In all these situations, the order in which things are placed is important. A change in the order creates a completely new arrangement. Permutations are the mathematical tool we use to count these arrangements. Understanding permutations helps us solve problems in scheduling, coding, security (like PINs and passwords), and even in planning events.

Lesson notes

Concept 1: What is a Permutation?

A permutation is an arrangement of objects in a specific order. The key phrase here is specific order. If the order changes, it becomes a different permutation. Example: Consider the letters A, B, and C. Arranging two letters at a time, we get: AB, BA, AC, CA, BC, CB. Notice that AB is different from BA. The order matters. There are 6 possible permutations (arrangements) of 2 letters chosen from the 3 available letters. Concept 2: Factorial Notation (!)

Before we can calculate complex permutations, we need to understand factorials. The factorial of a non-negative integer 'n', denoted by n!, is the product of all positive integers less than or equal to n. Formula: `n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1` Examples: `4! = 4 × 3 × 2 × 1 = 24` `6! = 6 × 5 × 4 × 3 × 2 × 1 = 720` Special Case: By definition, `0! = 1`. This is important for our formulas to work correctly. Concept 3: Permutations of 'n' distinct objects taken 'r' at a time (nPr)

This is the most common type of permutation problem. It answers the question: "From a group of 'n' different items, how many ways can we choose and arrange 'r' of them?" Formula: `nPr = n! / (n - r)!` Where: 'n' is the total number of objects available. 'r' is the number of objects we are selecting and arranging.

Evaluation guide

• Solve real life problems involving permutations.
• Group work, Talk for Learning, and Building on what others say.
• Permutation
• Learners in groups recall the concepts of arrangements or permutation as arranging objects where