Permutation and combination calculator

The permutation and combination calculator is a mathematical tool software specially used to calculate the number of permutation (Permutation) and the number of combination (Combination). Permutation and combination are core concepts in combinatorial mathematics and are widely used in fields such as probability statistics, cryptography, algorithm design, and lottery analysis.

Software features

Simple operation and friendly interface

The software interface design is simple and intuitive. Users only need to enter the total number of elements (n) and the number of selections (r) to calculate the number of permutations or combinations with one click. No complicated operations are required, and it is suitable for mathematics enthusiasts, students and professionals.

Supports multiple computing modes

The software provides two calculation modes: arrangement (taking order into consideration) and combination (not taking into account order), and users can switch freely according to needs. For example, choose permutations when calculating password combinations, and choose combinations when calculating lottery winning probabilities.

Real-time calculation and result display

After inputting the parameters, the software calculates and displays the results in real time, supporting large number operations to ensure accurate results. For example, calculate the number of combinations of 10 elements selected from 50 elements (C(50,10)), and the software can quickly give the result.

Formula and step display

Some software provides formula derivation and calculation steps to help users understand the principles of permutation and combination. For example, show the permutation number formula P(n,r) = n! / (n-r)! and the combination number formula C(n,r) = n! / (r!(n-r)!).

History and export functions

The software supports saving calculation history to facilitate users to review previous calculation results. Some software also provides an export function to save the results as text or Excel files for further analysis.

Multi-platform support

The software covers mainstream operating systems such as Windows, macOS, iOS, and Android, and users can use it on different devices. Some software also provides web version, which can be calculated online without installation.

Software function

Arrangement calculation

Input the total number of elements (n) and the number of selections (r), and calculate the number of permutations P(n,r).

Example: Calculate the number of permutations of selecting 3 out of 5 letters (P(5,3) = 60).

Combination calculation

Input the total number of elements (n) and the number of selections (r), and calculate the number of combinations C(n,r).

Example: Calculate the number of combinations of 4 out of 10 numbers (C(10,4) = 210).

Repeated arrangements and combinations

Supports calculation of permutations and combinations of repeatable elements.

Example: Count the number of permutations (3^2 = 9) that select 2 (repeatable) colors from 3 colors.

Probability calculation

Combining the permutation and combination results, calculate the probability of an event occurring.

Example: Calculate the probability of drawing 5 straight flush cards from 52 cards (need to combine the number of combinations and card type rules).

Batch calculation

Supports batch input parameters and calculates multiple permutation or combination results at one time.

Example: Input multiple sets of (n, r) values ​​and quickly generate a corresponding list of permutations or combinations.

Custom formulas and extended functions

Some software supports user-defined formulas or integrates other mathematical functions (such as factorial, logarithm, etc.).

Example: When calculating C(n,r), you can directly call the factorial function n!.

Visual display

Display calculation results in the form of charts or lists to help users intuitively understand the distribution of permutations and combinations.

Example: Shows the triangular distribution diagram of the combination number C(n,2) from 1 to 10.

FAQ

Parameter setting error:

Cause: The repeatability of the combination was not taken into account when setting the generator's parameters, or the correct boundary conditions, such as range limits or min/max values, were not set.

Solution: Choose whether to allow duplication according to specific needs, and clarify the required numerical boundaries to ensure that the parameters are set correctly.

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