What's the difference between nPr and nCr?

nPr (permutations) counts arrangements where order matters. nCr (combinations) counts selections where order doesn't matter. For example, choosing 3 people from 10: nPr considers ABC different from BAC, while nCr treats them as the same selection.

Why is nCr always less than or equal to nPr?

Because combinations don't distinguish between different orders of the same selection. For every combination, there are r! different permutations. So nPr = nCr × r!, making nCr = nPr ÷ r!.

What happens when r = n?

When r = n, you're selecting all items. nCr = 1 (only one way to select everything), while nPr = n! (n factorial ways to arrange all items).

Can r be greater than n?

No, you cannot choose more items than are available. Both nPr and nCr are undefined when r > n. The calculator will show an error for such inputs.

Permutation and Combination Calculator – nPr and nCr

Calculate permutations (nPr) and combinations (nCr) for probability and statistics problems. Understand arrangements and selections with detailed explanations.

Permutation and Combination Calculator – nPr and nCr

Calculate permutations (nPr) and combinations (nCr) for probability and statistics problems. Understand arrangements and selections with detailed explanations.

Calculation Type*

Choose calculation type

n (total items)*

Total number of items to choose from

r (items chosen)*

Number of items being chosen

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Math visualization will appear here

Permutations vs Combinations

Permutations and combinations are fundamental concepts in probability and statistics. The key difference is whether the order of selection matters.

When to Use Each

Use permutations when:

Order matters (arranging people in a line)
Positions are distinct (1st, 2nd, 3rd place)
Creating passwords or codes
Scheduling or sequencing problems

Use combinations when:

Order doesn't matter (selecting team members)
Choosing subsets from a group
Lottery number selection
Committee formation

How to Use This Calculator

Follow these simple steps to get accurate results:

Enter your calculation type
Enter your n (total items)
Enter your r (items chosen)
Click the "Calculate" button to see your results
Review the detailed breakdown and explanation

Why Use Our Permutation and Combination Calculator – nPr and nCr?

100% free and no registration required
Instant, accurate calculations with professional formulas
Mobile-friendly design that works on any device
Privacy-focused - your data never leaves your browser
Educational content to help you understand the results

Frequently Asked Questions

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