Calculation: The Combination Calculator is a helpful tool for determining the number of possible combinations from a given set of items.
What is the purpose of a Combination Calculator?
A Combination Calculator is used to find the total number of unique combinations of items, ensuring that order does not matter in the arrangement.
Combination Calculator formula?
The formula for calculating combinations is:
C(n, r) = n! / [r! * (n - r)!] Where:
- C(n, r) is the number of combinations,
- n is the total number of items,
- r is the number of items chosen,
- ! denotes factorial, which is the product of all positive integers up to that number.
Combination Calculator examplas
Example 1: Selecting 3 items from 5
Suppose you have 5 items and want to select 3 of them. Using the formula:
C(5, 3) = 5! / [3! * (5 - 3)!]- Calculate the factorials:
- 5! = 5 × 4 × 3 × 2 × 1 = 120
- 3! = 3 × 2 × 1 = 6
- (5 – 3)! = 2! = 2 × 1 = 2
- Substitute into the formula:
- C(5, 3) = 120 / (6 × 2) = 120 / 12 = 10
Thus, there are 10 unique combinations.
Example 2: Selecting 2 items from 6
Let’s calculate how many ways you can select 2 items from a set of 6:
C(6, 2) = 6! / [2! * (6 - 2)!]
- Calculate the factorials:
- 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
- 2! = 2 × 1 = 2
- (6 – 2)! = 4! = 4 × 3 × 2 × 1 = 24
- Substitute into the formula:
- C(6, 2) = 720 / (2 × 24) = 720 / 48 = 15
There are 15 unique combinations.
The Combination Calculator simplifies these steps by automating the calculations, making it an essential tool for mathematicians, statisticians, and students.