Combination Calculator
Calculate the number of possible combinations when selecting r items from a set of n items.
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Table of Contents
Combination Formula
Combinations are used when the order of selection doesn't matter. The formula for combinations is:
Where:
- n is the total number of items
- r is the number of items to select
- ! represents factorial
How to Calculate Combinations
To calculate combinations, follow these steps:
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1Calculate the factorial of n (n!)
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2Calculate the factorial of r (r!)
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3Calculate the factorial of (n-r) ((n-r)!)
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4Divide n! by the product of r! and (n-r)!
Understanding Combinations
Key points about combinations:
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1Order Doesn't Matter:
In combinations, the order of selection is not important. For example, selecting A,B,C is the same as selecting B,C,A.
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2No Repetition:
Each item can only be selected once in a combination.
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3Applications:
Combinations are used in probability, statistics, and various real-world scenarios like team selection, lottery numbers, etc.
Practical Examples
Example 1 Team Selection
Selecting 3 players from a team of 10 players
n = 10, r = 3
C(10,3) = 120
There are 120 ways to select 3 players from 10.
Example 2 Committee Formation
Forming a committee of 4 members from 8 candidates
n = 8, r = 4
C(8,4) = 70
There are 70 ways to form the committee.
Example 3 Lottery Numbers
Selecting 6 numbers from 49 possible numbers
n = 49, r = 6
C(49,6) = 13,983,816
There are 13,983,816 possible combinations.