What is the difference between permutation and combination?

Permutations count ordered arrangements (order matters). Combinations count unordered selections (order does not matter). For example, picking 3 team members from 10: order matters = 10P3 = 720; order does not matter = 10C3 = 120.

What is a master number in numerology?

Master numbers (11, 22, 33) are not reduced to single digits in numerology because they carry amplified spiritual significance. However, this tool covers permutations/combinations, not numerology.

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Permutation & Combination Calculator

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n - Total items

r - Items chosen

Permutation P(n,r)

n! / (n−r)! · Order matters

720

10! / (10−3)!

Combination C(n,r)

n! / (r!(n−r)!) · Order doesn't matter

120

10! / (3! × (10−3)!)

With Repetition Allowed

Ordered (n^r)

1,000

10^3

Unordered C(n+r−1,r)

220

C(12,3)

Word Arrangements

Enter a word

Unique arrangements of "MISSISSIPPI"

34,650

11! / (1! × 4! × 4! × 2!)

Letter frequencies: M×1, I×4, S×4, P×2

Pascal's Triangle (rows 0–8)

121

1331

14641

15101051

1615201561

172135352171

18285670562881

Highlighted cell: C(10,3)

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Calculate nPr and nCr simultaneously with formulas shown. Repetition modes, word arrangement with repeated letters, and Pascal's triangle up to row 8.

How to Use

1Enter n (total items) and r (items to choose)
2Click Calculate to see nPr (ordered) and nCr (unordered) simultaneously with formulas
3Scroll down for Pascal's Triangle (up to row 8) and repetition modes
4Word Arrangements: enter a word to see the number of distinct arrangements accounting for repeated letters
5Copy individual results using the copy buttons

Features

nPr and nCr calculated simultaneously
Formula display (factorial form)
Repetition modes: ordered (n^r), unordered C(n+r-1,r)
Word arrangements with repeated letters (multinomial coefficient)
Pascal's Triangle up to row 8
100% browser-based

Permutation & Combination Calculator

With Repetition Allowed

Word Arrangements

Pascal's Triangle (rows 0–8)

How to Use

Features

Frequently Asked Questions

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