What is the difference between permutation and combination?

Permutation (nPr) counts ordered arrangements — the order matters. Combination (nCr) counts selections where order does not matter. For example, choosing 3 players from 10 for positions (captain, vice-captain, secretary) is a permutation, while choosing 3 players for a team is a combination.

What is the formula for nPr and nCr?

nPr = n! / (n-r)! and nCr = n! / [r! × (n-r)!]. Here n is the total items and r is the items chosen.

Factorial (n!) is the product of all positive integers up to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By convention, 0! = 1.

Permutation & Combination Calculator — nPr & nCr

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Your Results

Permutation (nPr) 720

Formula 10! / (10-3)! = 10! / 7! = 720

nPr — Permutation 720

nCr — Combination 120

n! 3,628,800

r! 6

(n − r)! 5,040

Step-by-Step

nPr = n! / (n−r)! = 10! / 7! = 10 × 9 × 8 = 720

nCr = n! / [r! × (n−r)!] = 10! / (3! × 7!) = 720 / 6 = 120

What are Permutations and Combinations?

Permutations count the number of ways to arrange r items from n items when order matters. Combinations count selections when order does not matter.

Formulas

1. Permutation (nPr)

nPr = n! / (n − r)!

2. Combination (nCr)

nCr = n! / [r! × (n − r)!]

3. Factorial (n!)

n! = n × (n−1) × (n−2) × … × 2 × 1

0! = 1 (by convention)

Examples

nPr: Arrange 3 from 10: 10P3 = 720 ways (order matters).
nCr: Choose 3 from 10: 10C3 = 120 ways (order doesn't matter).
Lottery: Pick 6 from 49: 49C6 = 13,983,816 possible combinations.
PIN code: 4-digit PIN from 10 digits (with repetition): 10⁴ = 10,000.

When to Use Each

Permutation: Passwords, race rankings, seating arrangements, schedules.
Combination: Lottery, team selection, committee formation, card hands.

How This Calculator Works

Enter n and r: n = total items, r = items chosen (r ≤ n).
See results: nPr, nCr, and all factorials computed instantly.
Step-by-step: Detailed breakdown of the calculation shown below results.

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