Arrangements and groups: permutations and combinations
Grow the tree of arrangements to count who can win gold and silver, line friends up in a row, then see why a group of people is counted fewer times than an arrangement.
- UK: Year 12
- France: grade 12
- Iran: grade 10
- Afghanistan: grade 11
- Syria: grade 11
- Palestine: grade 10
- Ukraine: grade 11
- Russia: grade 9
Guide
This studio follows Afghan grade 11 chapter 9 (arrangements and the factorial n!, then combinations: choosing k of n when the order does not matter) and the UK A-level counting topic.
A branch of the tree is a choice, and a path from the start to an end is one arrangement. Once a person is used they cannot be chosen again, so the next stage has one branch fewer.
Common mistakes worked on here: adding the stages (4 + 3) instead of multiplying, using the same person twice, counting a group of people once for every order, and dividing by 3 instead of 3!.