Combinations — Choosing a Group (Grades 7–8)
When order does not matter — like picking a team of 2 from 4 friends — count combinations.
Understanding combinations — choosing a group
Choosing {A, B} is the same as {B, A}. To choose 2 from 4: there are 4 × 3 = 12 ordered pairs, but each group is counted twice, so 12 ÷ 2 = 6 combinations.
Seeing it in action
Worked example
How many ways to choose 2 friends from 4?
Ordered: 4 × 3 = 12. Each pair counted twice (order doesn't matter): 12 ÷ 2 = 6.
When order does not matter, remove duplicate orders.
A common mistake, and the fix
Counting the same group twice.
Picking Ana then Ben and picking Ben then Ana make one team, so the 12 ordered picks from 4 friends give only 12 ÷ 2 = 6 teams. Listing the pairs in order, AB, AC, AD, BC, BD and CD, is a good check.
Try a few
Choose 2 from 3
Choose 2 from 5
5×4÷2.
Choose 3 from 3
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
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