StudyBrixFree worksheets, study guides and courses

Mathematics · Grades 10–12

Combinations

Use combinations when order does not matter and items are chosen without replacement.

Make a worksheet

The key idea

Use combinations when order does not matter and items are chosen without replacement.

C(n,r) = n!/[r!(n − r)!]

Worked examples

How many different groups of 3 can be chosen from 10 distinct people, if order does not matter?

10!/(3! × 7!) = 120

120

How many different groups of 3 can be chosen from 11 distinct people, if order does not matter?

11!/(3! × 8!) = 165

165

Try it yourself

  1. How many different groups of 3 can be chosen from 11 distinct people, if order does not matter?

  2. How many different groups of 2 can be chosen from 5 distinct people, if order does not matter?

Check your understanding

Answers and marking notes
  1. 165

    11!/(3! × 8!) = 165

  2. 10

    5!/(2! × 3!) = 10

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.