Permutations & Combinations
P(n,r) = n!/(n-r)! counts ordered arrangements. C(n,r) = n!/(r!(n-r)!) counts unordered selections.
Examples
| Problem | Type | Answer |
|---|---|---|
| 3-digit PIN from 0-9 | P(10,3) | 720 |
| Pick 5 from 52 cards | C(52,5) | 2,598,960 |
| Arrange 4 books on shelf | P(4,4) = 4! | 24 |
How to Use This Permutation & Combination Calculator
Enter n (total items) and r (items chosen). Select permutation or combination. The calculator shows the count and the formula used.
Formula & How It Works
Permutation (order matters): P(n,r) = n! / (n-r)!. Combination (order does not matter): C(n,r) = n! / [r!(n-r)!].
Calculation Example
Choosing 3 from 10: Permutations P(10,3) = 720 (arrangements). Combinations C(10,3) = 120 (groups). A 6-digit PIN: P(10,6) = 151,200 (no repeats) or 10⁶ = 1,000,000 (with repeats).
Expert Tips
Ask: does order matter? Choosing club officers (president, VP, secretary) = permutation. Choosing a committee of 3 = combination. Lottery odds use combinations: C(49,6) = 13,983,816.
Frequently Asked Questions
Permutation vs combination?
Permutation: order matters (ABC ≠ BCA). Combination: order doesn't matter (ABC = BCA).
When to use each?
Use permutation for rankings, arrangements, passwords. Use combination for teams, groups, lottery.
What does n! mean?
n factorial = n × (n-1) × (n-2) × ... × 1. Example: 5! = 120.