10C3 Combination: Understanding the Concept
In mathematics, combinations are used to calculate the number of ways to choose items from a set without regard to the order of the items. One such combination is the 10C3 combination, which is essential in various mathematical and real-world applications. In this article, we will delve into the concept of 10C3 combination, its formula, and examples.
What is 10C3 Combination?
The 10C3 combination represents the number of ways to choose 3 items from a set of 10 items, without regard to the order of the items. This is denoted mathematically as:
10C3 = 10! / (3! * (10-3)!)
Formula for 10C3 Combination
The formula to calculate the 10C3 combination is:
10C3 = 10! / (3! * 7!)
where:
- 10! is the factorial of 10 (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)
- 3! is the factorial of 3 (3 × 2 × 1)
- 7! is the factorial of 7 (7 × 6 × 5 × 4 × 3 × 2 × 1)
Calculating 10C3 Combination
Using the formula, let's calculate the 10C3 combination:
10C3 = 10! / (3! * 7!) = (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / ((3 × 2 × 1) × (7 × 6 × 5 × 4 × 3 × 2 × 1)) = 120
Therefore, the 10C3 combination is 120, which means there are 120 ways to choose 3 items from a set of 10 items.
Real-World Applications
The 10C3 combination has several real-world applications, including:
Lottery Systems
In a lottery system, the 10C3 combination can be used to calculate the number of possible combinations of 3 numbers that can be drawn from a set of 10 numbers.
Data Analysis
In data analysis, the 10C3 combination can be used to calculate the number of ways to choose 3 variables from a set of 10 variables.
Cryptography
In cryptography, the 10C3 combination can be used to calculate the number of possible combinations of 3 keys from a set of 10 keys.
Conclusion
In conclusion, the 10C3 combination is an essential concept in mathematics, with various real-world applications. By understanding the formula and calculation of the 10C3 combination, we can apply it to solve various problems in different fields.
