The combination calculator determines the number of possible combinations that can be achieved by picking samples for a larger set. Our ncr calculator will also calculate every single combination of the database.

## What Is Number of Combinations?

**“It is a method of choosing items from a large set of objects without considering order and replacement.”**

In other words, the Combination calculator shows how many subsets are made from the larger set.

## Combination Formula:

The __combination formula__ calculator calculates the number of possible combinations by using the ncr formula given as:

$$nC_{r} = \dfrac{n!}{r!\left(n-r\right)!} $$

$$ C\left(n,r\right) = \dfrac{n!}{r!\left(n-r\right)!} $$

Where,

C(n,r) is the number of combinations.

n is the total number of elements in the set.

r is the number of the elements you choose from the set

! is the factorial sign

To find the factorial of the number, you can try our __factorial calculator__, which can help you to calculate the factorial of the number.

## How to Calculate Combinations?

The combinatorics calculator is the selection of the elements from the collection. Our n choose k calculator will give accurate calculations of all database elements. For a better understanding, look at the example below.

### Example # 1:

If I have 4 water bottles and I want to give these to the 8 people. Then how many ways can I give these 4 water bottles to the 8 people?

#### Solution:

As we already know that the formula for combinations is:

$$ C\left(n,r\right) = \dfrac{n!}{r!\left(n-r\right)!} $$

**Given Values:**

Total number of people (n) = 8

Chosen (r) = 4

So we have,

C(8,4) = 8!/4!(8-4)!

C(8,4) = 8!/4!(4)!

C(8,4) = 8*7*6*5*4!/4!(4)!

C(8,4) = 8*7*6*5/4!

C(8,4) = 8*7*6*5/4*3*2*1

C(8,4) = 1680/24

C(8,4) = 70

This is the final answer that you can verify from the combination calculator as well.

### Example # 2:

A demo was given by the 10 teachers in the college. The management wants to pick 5 out of 10 teachers on merit. How many different combinations does he pick?

#### Solution:

The combination equation is:

$$ C\left(n,r\right) = \dfrac{n!}{r!\left(n-r\right)!} $$

**Given Values:**

Total number of teachers (n) = 10

Chosen (r) = 5

So,

C(10,5) = 10!/5!(10-5)!

C(10,5) = 10!/5!(5)!

C(10,5) = 10*9*8*7*6*5!/5!(5)!

C(10,5) = 10*9*8*7*6/5!

C(10,5) = 10*9*8*7*6/5*4*3*2*1

C(10,5) = 30240/120

C(10,5) = 252

## Working of Combination Calculator:

Using the advanced combination solver is the way to choose the sample of r elements from a set of n distinct objects. These are the steps you ought to follow to get the instant results.

**Input:**

- Choose the number of elements of the database
- Enter the value of the total number of elements (n)
- Enter how many elements you want to choose (r)
- Choose one that you want to calculate (combinations, combinations with repetition)
- Hit the “calculate” button

**Output:**

- Combinations
- Combinations and repetition
- Step-by-step calculations

## FAQs:

### Does Repetition Matters In the Combination?

No, the order does not matter in the combination. The reason is that it is the selection of objects from a large set of objects without repetition.

### What Is The Difference Between Permutation And Combination?

**Permutation:** Different ways of arranging a set of items into sequential order.

Example: In the case of permutation, let’s suppose the door lock is 456 number. If we don’t care about the order, like the door look is 564 or 654, it will not work in this type of case. We need to enter the values 4-5-6 exactly.

**Combination:** Different ways of choosing items from a large set of objects, and in this case, the order doesn’t matters.

Example: In the case of combination, let’s suppose that I have a pen, marker, and copy. I can also say that I have a marker, pen, and copy, or I have copy, marker, and pen.

## References:

From the source Wikipedia: Combination, Number of k-combinations, Number of combinations with repetition, Number of k-combinations for all k, Probability: sampling a random combination, Number of ways to put objects into bins.