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 Combinations Calculator?
'Cuemath's combinations calculator' is an online tool that assists in calculating the number of possible combinations of selecting a sample of r elements from a set of n distinct objects. Cuemath's online combinations calculator helps you to calculate the number of combinations in a few seconds.
How to Use Combinations Calculator?
Please follow the below steps to find the number of combinations:
- Step 1: Enter the total number of objects, and the sample size 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 Combinations Calculator?
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 as 'n choose r'. To determine the number of combinations the following formula is used:
C(n,r) = n!/(r!(n-r)!)
It is read as the number of possible combinations of selecting a sample r from n distinct objects.
Find the number of ways in which 6 balls can be selected from a bag containing 9 different colored balls
Total number of balls = 9
Required Sample size = 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.