Ask first whether the order matters
Positions in a race are different if the order changes — that is a permutation. Members of a team are not — that is a combination, and there are always fewer of them.
Class 11 · 24 games
Counting arrangements, explained with pictures
Counting how many ways something can be arranged or chosen.
In everyday life: How many different teams of 5 you could pick from a class of 11.
Multiply the choices at each step
3 shirts and 4 trousers give 3 x 4 = 12 outfits. Every choice you make multiplies, it does not add.
A worked example
How many ways can you choose 2 students from 4?
6
There are 4 x 3 = 12 ordered picks, but choosing A then B is the same pair as B then A, so halve it.
Words to know
- permutation
- An arrangement where the order counts.
- combination
- A selection where the order does not count.
In the games
You will decide whether order matters and pick the correct count for a situation.
Skills
- Permutations and combinations · Class 11
- The binomial theorem · Class 11
By class
Practise counting arrangements in Tivumo
No download, no account for your child. Classes 3 to 12, more than 1,000 games.