Combination Calculation

1. Enter the "total number (n)" to be extracted.
2. Enter the "number of items (r) to be extracted from the total number (n).
3. The "number of combinations" and the "number of permutations" as reference data will be calculated automatically.

Combinatorial calculation is a calculation that calculates the total number of ways to select a specific number of elements from a collection of different elements. It is characterized by the fact that the order of selection is not taken into consideration. Combinatorial calculation is often used in mathematics and statistics and plays an important role in various situations.

Uses of combination calculations

• Lottery and rafflesCalculate the probability of choosing a specific number of winning numbers
• Card gamesFind combinations when drawing a specific number of cards from a deck
• Product combinationsWhen selecting several products from multiple products to create a set
• Statistics and probability theoryCalculate the number of patterns when selecting a sample

Differences from permutations

Combinations do not take into account the order of selection. Permutations, on the other hand, are different in that they take into account the order of selection. For example, {A, B} and {B, A} are counted as the same in combinations, but different in permutations.

Calculate the number of combinations where r elements are selected from n elements.

n! is the factorial of n, r! is the factorial of r, and (n - r)! is the factorial of (n - r).

A factorial is the result of multiplying a positive integer by all integers from that integer to 1. Factorials are expressed using the symbol "!".

Example: Selecting 2 out of 5 elements

5C2 = 5 ​​× 4 2 × 1 = 10

This tool is available for free.