Permutation Calculator (nPr)
Use this to calculate ordered arrangements: nPr = n! / (n-r)!.
Tip: For valid permutations, use whole numbers with 0 ≤ r ≤ n.
What does permutation mean?
A permutation counts how many different ordered ways you can choose items from a group. The key phrase is “order matters.” If you pick A then B, that is different from B then A.
In symbols, we write permutation as nPr, where:
- n = total number of available items
- r = number of items you choose
Permutation vs. combination
Students often confuse permutations with combinations. Here is the quick distinction:
- Permutation (nPr): order matters
- Combination (nCr): order does not matter
Example: Choosing class president and vice president is a permutation problem because those roles are different. Choosing any 2 students for a committee is a combination problem because role order is irrelevant.
The formula behind your calculator’s nPr button
Most scientific calculators compute permutations with:
nPr = n! / (n-r)!
You can also think of it as multiplying descending values:
nPr = n × (n-1) × (n-2) ... for r factors
For example, 10P3 = 10 × 9 × 8 = 720.
How to do permutation on a scientific calculator
General steps
- Enter n
- Press the nPr function (often under MATH, PRB, or SHIFT menu)
- Enter r
- Press equals
If you do not see nPr directly
Some calculators hide nPr as a secondary function. Try the SHIFT or 2nd key first. If your calculator still does not provide nPr, use manual multiplication or factorial formula entry.
Worked examples
Example 1: Podium winners
There are 12 runners, and you want gold, silver, and bronze positions. That is 12P3:
12P3 = 12 × 11 × 10 = 1320
Example 2: 4-digit lock code from 10 digits without repetition
Order matters in a code, so this is 10P4:
10P4 = 10 × 9 × 8 × 7 = 5040
Example 3: Team captain and co-captain
From 8 players, assign two distinct roles:
8P2 = 8 × 7 = 56
Common mistakes and how to avoid them
- Using nCr instead of nPr: Ask yourself whether order/position matters.
- Swapping n and r: n is total pool, r is chosen count.
- Trying r > n: Not possible for basic no-repetition permutation.
- Using decimals: Standard permutation uses whole numbers only.
When is permutation useful in real life?
Permutations show up in scheduling, rankings, role assignment, coding, and security contexts. Any scenario where sequence matters can often be modeled with nPr.
- Ranking contest winners
- Assigning job titles from a candidate pool
- Generating ordered passwords or PIN-like arrangements
- Planning seating or speaking orders
Manual method when no nPr key exists
If your calculator lacks nPr, multiply the descending values for r terms:
nPr = n × (n-1) × ... × (n-r+1)
For 15P4, multiply 15 × 14 × 13 × 12 to get 32,760.
Quick FAQ
Can r equal 0?
Yes. nP0 = 1, because there is exactly one way to choose nothing.
Can n and r be the same?
Yes. nPn = n!, since you are arranging all items.
Does this calculator handle large values?
Yes, this page uses big integer arithmetic for exact integer results. Very large inputs may take longer, so practical limits are applied for speed.
Bottom line
To do permutation on a calculator, identify n and r, confirm order matters, and use nPr. If the key is hidden, use the formula or descending multiplication. Use the calculator above to check your work quickly and avoid common input errors.