Number Theory
Combinations - Number Theory
Learn the combinations with examples, step-by-step guide, and calculator tools. Number of ways to choose r items from n
The combinations is a fundamental concept in number theory. Number of ways to choose r items from n. This page provides a comprehensive guide with worked examples and practical applications.
The Formula
\[C(n,r) = \binom{n}{r} = \frac{n!}{r!(n-r)!}\]
Variables
C(n,r)
Combinations
n
Total items
r
Items to choose
Step-by-Step Guide
- 1
Step 1: Gather your data values
- 2
Step 2: Apply the formula
- 3
Step 3: Perform the calculations
- 4
Step 4: Interpret the result
Examples
Example 1
Example 1: [] → C(5,2) = 5!/(2!×3!) = 120/(2×6) = 10
Example 2
Example 2: 10
Frequently Asked Questions
What is the combinations?
Number of ways to choose r items from n
How do I calculate combinations?
Use the formula: C(n,r) = \binom{n}{r} = \frac{n!}{r!(n-r)!}. Follow the steps provided above.
What tools can help with combinations?
We provide online calculators: calculator