Description
What changes when the group matters, but the order does not?
In Lesson 4 of Counting & Combinatorics, learners compare arrangements with selections such as teams, committees and pizza toppings. They see why Alice–Ben and Ben–Alice describe the same team and why ordered counting can overcount.
The lesson develops from choosing two people to choosing larger groups, leading to combination notation and the idea of dividing by the orders that do not matter.
This lesson includes
- practice deciding whether order matters;
- two-person team examples showing duplicate ordered choices;
- choosing larger groups by arranging first and dividing by unwanted orders;
- combination notation;
- the symmetry between choosing what stays and choosing what is left out;
- team, committee and pizza-topping problems;
- answers and discussion;
- supplementary exercises for extra practice and revision.
Suitable for learners aged 10 and over. Lesson 3 on arrangements is recommended first.
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This is Lesson 4 of the 6-part Beyond Curriculum: Counting & Combinatorics course.
