BMTS413-2026

BMTS413
Counting Techniques

ECTS Value: 3 ECTS

Contact Hours: 15

Self Study Hours: 36

Assessment Hours: 24

Overall Objectives and Outcomes

This module revisits the fundamental principles and methods used to solve counting problems in mathematics, including the key concepts of permutations and combinations. Throughout the module, course participants will distinguish between combinations and permutations and apply the appropriate tools to solve a wide range of problems, ranging from arranging objects in a linear or a circular arrangement, to selecting groups from larger sets, with or without repetitions. These skills are essential for understanding more complex topics in mathematics, computer science, and probability.

This module is ideal for course participants with a basic understanding of algebra and an interest in mathematical problem-solving and is aimed at enhancing their understanding in preparing them to design appropriate activities, lessons and assessments in this topic at post-secondary education levels.

By the end of this module, the learner will be able to:

Competences

- a)Support others in learning and applying the meaning and practical uses of different counting techniques;
- b)Create lesson plans and/or resource packs for teaching this topic;
- c)Design relevant assessment tasks to supervise students’ understanding of this topic.

Knowledge

- - a)State the fundamental principle of counting;
  - b) $n!$
  - c)Define a permutation as an ordered arrangement of a number of items;
  - d)Define a combination as an unordered selection of a number of items from a given set;
  - e)Distinguish between permutations and combinations when presented with counting problems to solve.

Skills

- - a)Distinguish between permutations and combinations when presented with counting problems to solve;
  - b)Apply their knowledge about combinations as an unordered selection of a number of items and solve related counting problems;
  - c)Derive and explain the relationship between combinations and permutations;
  - d)Solve simple probability problems involving permutations and combinations.

Assessment Methods

This module will be assessed through: Assessment Tasks, Lesson Plan