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