Permutations and Combinations

This topic focuses on counting techniques essential in probability and combinatorics. Learners will study permutations (arrangements) and combinations (selections), understanding their formulas and applications.

Learning Outcomes:
The learner should be able to:

• Differentiate between permutations and combinations.
• Arrange sets of different objects in a row to distinguish between different arrangements.
• Demonstrate how to arrange a number of different objects in turn to derive the relationship between the factorial notation (!) and number of arrangements.
• perform arrangements of a number of different items to discover that the arrangement of 𝑟 out of n objects in a row is given by the formula nPr.
• Form permutations involving: i) identical objects, ii) with or without repetition, iii) with restrictions, iv) circular arrangements.
• Select a set of 2 items from 2, 3 or 4 items to form a group.
• Illustrate how a group of 𝑟 items can be selected from n items to form a combination.
• Develop the formula nCr used for selecting 𝑟 objects from n objects to form a group.
• Recognise the difference between permutations and combinations scenarios.
• Apply knowledge of permutations and combinations in various real-world situations like creation of passwords, pin numbers, team selections, planning menus or outfits etc.