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# n Choose k Calculator

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

## What is n Choose k Calculator?

'**n Choose k Calculator**' is an online tool that assists in calculating the number of possible combinations of selecting a sample of k elements from a set of n distinct objects. Online n Choose k Calculator helps you to calculate the number of combinations in a few seconds.

### n Choose k Calculator

## How to Use n Choose k Calculator?

Please follow the steps below on how to use the calculator:

**Step 1:**Enter the total number of objects(n), and the sample size(k) in the given input boxes.**Step 2:**Click on the**"Calculate"**button to find the number of combinations.**Step 3:**Click on the**"Reset"**button to clear the fields and enter the different values.

## How to Find the Combinations?

The combinations are defined as the number of ways in which a sample of r elements can be selected from n distinct objects that's why it is also referred to as 'n choose k'. To determine the number of combinations the following formula is used:

**C(n, k) = n!/(k!(n - k)!)**

It is read as the number of possible combinations of selecting a sample 'k' from 'n' distinct objects.

**Solved Examples on n Choose k Calculator**

**Example 1:**

Find the number of ways in which 6 balls can be selected from a bag containing 9 different colored balls

**Solution:**

Total number of balls = 9

Required Sample size = 6

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

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 3 balls can be selected from a bag containing 7 different colored balls

**Solution:**

Total number of balls = 7

Required Sample size = 3

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

C(7,3) = 7!/(3!(7-3)!)

C(7,3) = 7!/(3!(4)!)

C(7,3) = 35.

Therefore, the total number of combinations to select 3 balls from a bag of 7 balls is 35.

**Example 3:**

Find the number of ways in which 10 balls can be selected from a bag containing 15 different colored balls

**Solution:**

Total number of balls = 15

Required Sample size = 10

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

C(15, 10) = 15!/(10!(15-10)!)

C(15, 10) = 15!/(10!(5)!)

C(15, 10) = 3003

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

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

- Number of objects(n) = 10 and sample size(k) = 5
- Number of objects(n) = 15 and sample size(k) = 4

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