On a TI-84 Plus CE
- Type n, then MATH → PROB → nCr (or nPr), then r, then ENTER.
Tip: nCr ignores order (choosing a team); nPr counts order (ranking places). nCr(n, r) is the binomial coefficient.
Permutations and combinations (nPr, nCr)
Count arrangements and selections quickly - and get the coefficients used in the binomial theorem.
In short: Permutations count ordered arrangements and combinations count selections where order does not matter, written nPr and nCr. The GDC has dedicated functions for both: enter n, choose nPr or nCr, then enter r. Decide first whether order matters in the question, because choosing the wrong one gives a different answer.
When you'd use this
- Counting the number of ways to arrange items where order matters (permutations).
- Counting the number of ways to choose items where order doesn't matter (combinations).
- Finding a binomial coefficient for the binomial expansion or binomial distribution.
- A probability question that starts with "how many ways can..." before the actual probability.
At a glance: TI-84 Plus CE, Casio fx-CG50 and TI-Nspire CX compared
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | Type n, then MATH → PROB → nCr (or nPr), then r, then ENTER. | Type n, then OPTN → PROB → nCr (or nPr), then r. | Use nCr(n, r) or nPr(n, r) from the catalog. |
On a Casio fx-CG50 and fx-CG100
- Type n, then OPTN → PROB → nCr (or nPr), then r.
Tip: nCr ignores order (choosing a team); nPr counts order (ranking places). nCr(n, r) is the binomial coefficient.
On a TI-Nspire CX
- Use nCr(n, r) or nPr(n, r) from the catalog.
Tip: nCr ignores order (choosing a team); nPr counts order (ranking places). nCr(n, r) is the binomial coefficient.
Related guides
Try it yourself
Here's a real IB-style question that uses exactly this technique.
Easy
Calculator
Paper 2
[3 marks]
From 8 people, find (a) the number of ways to choose a committee of 3, and (b) the number of ways to choose a president, secretary and treasurer (3 different roles).
(a) 56 (b) 336
Mark it
Correct
3 / 3 marks
Worked solution & mark scheme:
M1 8C3 for the committee (order doesn't matter)
A1 56
M1 8P3 for the 3 distinct roles (order matters)
A1 336
Common questions
When would I need to calculate permutations and combinations (nPr and nCr) in IB Maths?
Count arrangements and selections quickly - and get the coefficients used in the binomial theorem. Counting the number of ways to arrange items where order matters (permutations). Counting the number of ways to choose items where order doesn't matter (combinations).
How do I calculate permutations and combinations (nPr and nCr) on a TI-84 Plus CE?
1. Type n, then MATH → PROB → nCr (or nPr), then r, then ENTER.
How do I calculate permutations and combinations (nPr and nCr) on a Casio fx-CG50 and fx-CG100?
1. Type n, then OPTN → PROB → nCr (or nPr), then r.
How do I calculate permutations and combinations (nPr and nCr) on a TI-Nspire CX?
1. Use nCr(n, r) or nPr(n, r) from the catalog.
What should I watch out for when I calculate permutations and combinations (nPr and nCr)?
nCr ignores order (choosing a team); nPr counts order (ranking places). nCr(n, r) is the binomial coefficient.
How are marks awarded when I calculate permutations and combinations (nPr and nCr) in an IB exam?
In the worked example on this page (3 marks, Paper 2), the marks are: M1: 8C3 for the committee (order doesn't matter); A1: 56; M1: 8P3 for the 3 distinct roles (order matters); A1: 336.
Practise with your calculator
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.