StatisticsProbability
Permutations (nPr) & Combinations (nCr) Calculator
Calculate how many ways you can arrange or choose r items from a set of n elements. Computes nPr, nCr, and factorials.
Set Size and Selections
Combinations (Order Does Not Matter)
C(10, 4) = 210
Ways to choose 4 items out of 10 without regard to order.
Permutations P(10, 4) (Order matters):5,040
Factorial n! (10!):3,628,800
Mathematical Formula: nPr & nCr Formulas
P(n, r) = n! / (n - r)! | C(n, r) = n! / [r!(n - r)!]
Combinatorics equations for ordered arrangements (permutations) vs unordered selections (combinations).
How to Use This Calculator
- 1Enter total items (n) and selected items (r).
- 2Click Calculate.
- 3Review both Permutations (Order matters) and Combinations (Order does not matter) alongside factorials.
Practical Example: Lottery / Team Selection
Scenario: Choosing a 4-person committee from a group of 10 people (n=10, r=4).
n (Total):10
r (Chosen):4
Result: Combinations (nCr): 210 ways | Permutations (nPr): 5,040 ways
There are 210 distinct groups of 4 people, but 5,040 ways if specific job titles (president, VP, etc.) are assigned.
Frequently Asked Questions
Use Permutations when order is important (e.g., race podium 1st, 2nd, 3rd, or passwords). Use Combinations when grouping order does not matter (e.g., poker hands or team rosters).
Pro Calculation Tips
- Remember: A combination lock is actually a permutation lock, because the order of numbers matters!
Model Assumptions
- Items n and r must be non-negative integers with r ≤ n.