Combinations Permutations
Use this free Combinations Permutations to quickly get accurate results in seconds, free and instantly offline with no signup required ever, trusted by professionals in Austin, Chicago, Miami, Denver, Seattle, and New York for reliable daily use without accounts, subscriptions, limits, or delays on any device for everyday personal and business workflows daily.
Calculate combinations and permutations.
Calculator Inputs
About Comb Perm
Use this free Combinations Permutations to quickly get accurate results in seconds, free and instantly offline with no signup required ever, trusted by professionals in Austin, Chicago, Miami, Denver, Seattle, and New York for reliable daily use without accounts, subscriptions, limits, or delays on any device for everyday personal and business workflows daily.
How selection math works in seconds: Enter n items with r picks to get combinations plus permutations side by side with factorial steps together. Results appear at $0 cost in your browser.
Why both matter for USA decisions on 09/22/2026: Committees ignore order; passwords depend on it — same numbers, wildly different counts. Austin commissioners setting $50,000 fantasy drafts value pick slots. New York players chasing $300M jackpots face combinatorial reality.
Audit sampling: Chicago auditors sampling $9M transaction populations size samples statistically. Denver juries pooling civic panels randomize fairly.
Gala charts: Miami planners seating $400,000 charity galas arrange tables combinatorially. Seattle password policies enforcing $4M security rules mandate lengths.
Factorial guards: Beyond twenty items, exact integers need big-number libraries — floats round silently.
Nonprofit seats: Boston boards filling $900,000 governance slates stagger terms combinatorially. Chicago choirs arranging $150,000 riser formations voice sections evenly on 09/22/2026.
Award slates: Miami film festivals jurying $2M award shortlists deliberate blindly. Phoenix utilities rotating $300,000 storm crews cover territories.
Rescue grids: Denver search teams gridding $400,000 backcountry sectors assign probabilities. Replacement flags change counts enormously.
Where it is used
Austin fantasy commissioners set $50,000 league drafts, Chicago auditors sample $9M transaction populations, Miami event planners seat $400,000 gala charts, Denver juries pool $0 civic panels, Seattle password policies enforce $4M entropy rules, and New York lottery players chase $300M jackpots. Selection math counts Boston boards fill $900,000 nonprofit seats, Chicago choirs arrange $150,000 riser formations, Miami film festivals jury $2M award slates, Denver search teams grid $400,000 rescue sectors, and Phoenix utilities rotate $300,000 outage crews.
How to use the Comb Perm
- Total Items (n) — enter the value (e.g. 10).
- Select Items (r) — enter the value (e.g. 3).
- Calculate — press the Calculate button to see the result instantly above.
Formula
P(n,r) = n! / (n-r)! C(n,r) = n! / (r! * (n-r)!)
Examples
Draft order
Jackpot odds
Password space
Frequently Asked Questions
- When should I use permutations versus combinations for combinations permutations?
- Use permutations when the order of selection matters, such as arranging items, forming passwords, or ranking candidates. Use combinations when order does not matter, such as selecting a committee, choosing lottery numbers, or picking items from a menu. The key question is whether rearranging the same items creates a different combinations permutations outcome.
- Why are permutations always greater than or equal to combinations for combinations permutations?
- Permutations count every possible arrangement of the selected items, while combinations count each unique group only once. Since each combination of r items can be arranged in r factorial different ways, permutations equal combinations multiplied by r factorial. This relationship is fundamental to combinations permutations counting problems.
- What is the difference between permutations with and without repetition for combinations permutations?
- Without repetition, each item can be selected only once. With repetition, items can be reused. For example, a 4-digit PIN allows repetition, while selecting 4 cards from a deck does not. The Combinations Permutations computes permutations and combinations without repetition for accurate combinations permutations results.
- How are permutations and combinations used in combinations permutations probability?
- To find the probability of a specific outcome, divide the number of favorable arrangements by the total number of possible arrangements. This approach solves problems ranging from card games to quality control, making combinations permutations probability calculations systematic and accurate.
- Can I use the Combinations Permutations for lottery odds calculations?
- Yes, lottery odds are calculated using combinations. For example, choosing 6 numbers from 49 gives over 13.9 million possible combinations, meaning the odds of matching all six are approximately 1 in 14 million. Use the combinations result to understand your chances in any combinations permutations lottery or random selection scenario.