Combination — Precalculus, what it means and where it is taught
A selection where order does not matter. C(n,r) = n!r!(n-r)!.
Taught in Precalculus.
Where it is taught
What uses it later
This idea is needed for:
- Binomial theorem — The rule expanding (a+b)n using combinations as coefficients.
Practise this idea
4 questions in the course bank use Combination, in Triangle Congruence Proofs, Counting, Permutations & the Binomial Theorem.
Problem 1
Which combination does NOT prove congruence?
- SSA
- SSS
- ASA
- AAS
Worked answer
SSA
SSA can give two different triangles.
It proves nothing.
Problem 2
A committee of 3 is chosen from 8 people. Which applies?
- A combination
- A permutation
- Neither
- Both give the same
Worked answer
A combination
No, so order does not matter
Problem 3
Gold, silver and bronze are awarded to 3 of 8 runners. Which applies?
- A permutation
- A combination
- Neither
- Both give the same
Worked answer
A permutation
Yes, so order matters
Problem 4
A bag has 5 red and 3 blue marbles. Two are drawn at once. What is the probability both are red? Give a fraction in lowest terms.
Worked answer
5/14
C(5,2)C(8,2) = 1028
= 514