​Combination Calculator
​Calculate the number of combinations with or without repetition using the Combination Calculator. Choose n and r values to find the total combinations. Fast and accurate results.
Combination Calculator
How to Use Combination Calculator
​To use the Combination Calculator, follow these steps:
Example 1: Without Repetition Suppose you have 6 items (n) and you want to choose 3 items (r) without repetition.
Example 2: With Repetition Suppose you have 4 different items (n) and you want to choose 2 items (r) with repetition allowed.
- Enter the total number of items (n).
- Enter the number of items to select (r).
- Choose whether to include repetition or not by selecting the appropriate option.
- Click the "Calculate" button.
- The calculator will display the number of combinations based on your input.
Example 1: Without Repetition Suppose you have 6 items (n) and you want to choose 3 items (r) without repetition.
- Enter n = 6 and r = 3.
- Choose "No Repetition" option.
- Click "Calculate."
- The calculator will display the result: "Number of combinations: 20." Explanation: There are 20 different ways to choose 3 items from a set of 6 items without repetition.
Example 2: With Repetition Suppose you have 4 different items (n) and you want to choose 2 items (r) with repetition allowed.
- Enter n = 4 and r = 2.
- Choose "With Repetition" option.
- Click "Calculate."
- The calculator will display the result: "Number of combinations with repetition: 10." Explanation: There are 10 different ways to choose 2 items from a set of 4 items with repetition allowed.
About Combination Calculation
​Combination calculation is a mathematical concept used to determine the number of ways to select a specific number of items from a larger set, considering whether repetition is allowed or not. It is commonly applied in probability, statistics, and combinatorics.
When considering combinations without repetition, each item can be chosen only once. For example, let's take the set of letters {A, B, C, D}. If we want to select 2 letters without repetition, the possible combinations are AB, AC, AD, BC, BD, and CD. In this case, the order of selection does not matter, so AB is the same as BA. The total number of combinations without repetition is 6.
On the other hand, when considering combinations with repetition, an item can be chosen multiple times. Using the same set of letters {A, B, C, D}, but now allowing repetition, the possible combinations for selecting 2 letters are AA, AB, AC, AD, BB, BC, BD, CC, CD, and DD. Again, the order of selection does not matter. The total number of combinations with repetition is 10.
To calculate combinations, you can use the combination calculator. Simply input the total number of items (n) and the number of items to be selected (r). Additionally, you can specify whether repetition is allowed or not. The calculator will compute the number of combinations accordingly. This calculation helps in understanding the various ways items can be chosen from a set, aiding in decision-making and solving combinatorial problems.
When considering combinations without repetition, each item can be chosen only once. For example, let's take the set of letters {A, B, C, D}. If we want to select 2 letters without repetition, the possible combinations are AB, AC, AD, BC, BD, and CD. In this case, the order of selection does not matter, so AB is the same as BA. The total number of combinations without repetition is 6.
On the other hand, when considering combinations with repetition, an item can be chosen multiple times. Using the same set of letters {A, B, C, D}, but now allowing repetition, the possible combinations for selecting 2 letters are AA, AB, AC, AD, BB, BC, BD, CC, CD, and DD. Again, the order of selection does not matter. The total number of combinations with repetition is 10.
To calculate combinations, you can use the combination calculator. Simply input the total number of items (n) and the number of items to be selected (r). Additionally, you can specify whether repetition is allowed or not. The calculator will compute the number of combinations accordingly. This calculation helps in understanding the various ways items can be chosen from a set, aiding in decision-making and solving combinatorial problems.