Tool Master

Combinatorics Calculator & Simulator

Permutation without repetitionP(n) = n!

Number of all possible orderings of n distinct elements.

Permutation with repetitionP_n^(k1,k2...)

Ordering of n elements where items repeat k1, k2... times.

Variation without repetitionV(n, k) = n! / (n-k)!

Selecting k elements from n where order matters and items cannot repeat.

Variation with repetitionV_k^i(n) = n^k

Selecting k elements from n where order matters and items can repeat.

Combination without repetitionC(n, k)

Selecting k elements from n where order does not matter and items cannot repeat.

Combination with repetitionC_k^i(n) = C(n+k-1, k)

Selecting k elements from n where order does not matter and items can repeat.

Parameter Settings
Max: 100
Practical Example & Description
Example: In how many ways can 5 people sit on a bench? Every person occupies a distinct seat.
Dynamic element arrangement:
A B C D E
Calculation Result
P(5) = 5!
Total possible outcomes:
120
3 digits
Calculation Steps & Breakdown:
  • 5! = 5 × 4 × 3 × 2 × 1 = 120
Version 1.9.3

Cookie & Privacy Preference

This site uses Local Storage for essential UI functionality (saving form values, theme, language). With your consent, we use Google Analytics 4 for anonymous traffic statistics.