Math

Permutation and Combination Calculator

Find nPr (permutations) and nCr (combinations).

Calculated Output

Permutations nPr 720

Combinations nCr 120

Formula: nPr = n!/(n−r)!, nCr = n!/(r!(n−r)!)

Step-by-Step Breakdown

1. Values used:

2. n (total items) = 10

3. r (chosen items) = 3

5. Permutations nPr = 720

6. Combinations nCr = 120

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The math behind it

nPr = n!/(n−r)! counts arrangements where order matters. nCr = nPr ÷ r! removes the ordering, counting selections.

From 10 items choose 3: nPr = 720, nCr = 120.

When do I use which?

Use permutations when order matters (e.g. rankings), combinations when it doesn't (e.g. lottery picks).