Permutation & Combination Calculator

Calculate permutations (nPr) and combinations (nCr) for counting problems.

Total Items (n)

Items Chosen (r)

Results

Permutation nPr720

Combination nCr120

n!36,28,800

r!6

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What is Permutation & Combination?

Permutations count arrangements where order matters. Combinations count selections where order doesn't matter.

Example: Choosing 3 people from 10 for president, VP, and secretary (order matters) = permutation. Choosing 3 people for a committee (order doesn't matter) = combination.

Formula

Permutation: nPr = n! / (n-r)! Combination: nCr = n! / (r! × (n-r)!)

Factorial: n! = n × (n-1) × (n-2) × ... × 1

Example: 10P3 = 10!/7! = 720 10C3 = 10!/(3!×7!) = 120

How to use this Permutation & Combination Calculator?

1. Enter total items (n). 2. Enter items to choose (r). 3. See both permutation and combination results.

Frequently asked questions

When to use permutation vs combination?

Permutation: order matters (arranging, ranking, passwords). Combination: order doesn't matter (teams, committees, lottery).

What is factorial?

n! = n × (n-1) × ... × 1. For example: 5! = 120, 10! = 3,628,800. 0! = 1 by convention.

How many lottery combinations?

For a 6/49 lottery: 49C6 = 13,983,816 combinations. Your probability of winning = 1 in ~14 million.

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