# Combinations Calculator

Combinations Calculator calculates the possible combinations for the given number of objects and sample size. Combinations is a mathematical technique that determines the number of possible ways to select objects from a collection of items where the order of selection does not matter.

## What is Combinations Calculator?

Combinations Calculator is an online tool that assists in calculating the number of possible combinations of selecting r elements from a set of n distinct objects. Combinations are used in scenarios where a selection can be made without arranging the objects. To use this * combinations calculator*, enter the values in the input boxes.

### Combinations Calculator

*Use 2 digits only.

## How to Use Combinations Calculator?

Please follow the steps below to find the number of combinations using an online combinations calculator:

**Step 1:**Go to Cuemath’s online combinations calculator.**Step 2:**Enter the total number of objects, and the sample size in the given input box of the combinations calculator.**Step 3:**Click on the**"Calculate"****Step 4:**Click on the**"Reset"**

## How Does Combinations Calculator Work?

Suppose we have a situation where we want to create a committee of 3 members out of a total of 18 members. We are free to select any 3 members. Thus, to select these 3 members we will use combinations. This is because we do not need to order or arrange the members while selecting them. On the other hand, permutations refer to the arrangement of elements in a particular order or sequence. Both permutations and combinations are techniques deployed for counting items. They are also used to determine how many outcomes are possible in any given situation. When we need to make an arrangement, permutations are used. Similarly, when a selection has to be made combinations are utilized. Given below is the formula for combinations:

C (n, r) = n! / r! (n - r)!

C (n,r) is known as the binomial coefficient.

n = the total number of objects.

r = the number of objects that are selected.

The combinations formula is used to give the number of ways in which r objects can be selected from n objects.

## Solved Examples on Combinations

**Example 1:** Find the number of ways in which 6 balls can be selected from a bag containing 9 different colored balls and verify it using the combinations calculator.

**Solution:**

Total number of balls, n = 9

Required Sample size, r = 6

Number of combinations = C(n,r) = n! / r! (n-r)!

C(9,6) = 9! / 6! (9-6)!

C(9,6) = 9!/ 6! (3)!

C(9,6) = 84

Therefore, the total number of combinations to select 6 balls from a bag of 9 balls is 84.

**Example 2:** Find the number of ways in which 7 people can be selected from a group of 18 for a soccer match and verify it using the combinations calculator.

**Solution:**

Total number of balls, n = 18

Required Sample size, r = 7

Number of combinations = C(n,r) = n! / r! (n-r)!

C(18,7) = 18! / 7! (18-7)!

C(18,7) = 18! / 7! (11)!

C(18,7) = 31824

Therefore, the total number of combinations to select 7 people from a group of 18 people is 31824.

Similarly, you can try the combinations calculator to find the possible number of combinations for the following:

- Find the number of ways in which 7 chocolates can be selected from a box containing 11 chocolates.
- Find the number of ways in which 15 pebbles can be selected from a bag containing 22 different colored pebbles.

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