How to Calculate Factorials: Complete Mathematics Guide
Learn how to calculate factorials and understand their applications. Master factorial notation, solve permutation and combination problems, and apply factorials to real-world scenarios.
🔢 How to Calculate Factorials: Complete Guide
Factorials are fundamental mathematical operations that appear frequently in probability, statistics, and combinatorics. Understanding how to calculate factorials is essential for solving permutation and combination problems.
📚 Factorial Definition
Notation and Formula
n! = n × (n-1) × (n-2) × ... × 2 × 1
Special Cases:
- 0! = 1 (by definition)
- 1! = 1
🎨 Example Calculations
Example 1: 5!
- 5! = 5 × 4 × 3 × 2 × 1 = 120
Example 2: 7!
- 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
Example 3: 10!
- 10! = 3,628,800
🌍 Applications
Permutations
Number of ways to arrange n objects: P(n) = n!
Example: 5 books on shelf = 5! = 120 arrangements
Combinations
Choose r objects from n: C(n,r) = (n!)/(r!(n-r)!)
Example: Choose 3 from 5 = (5!)/(3!2!) = 10 ways
Probability
- Lottery calculations
- Card game odds
- Tournament brackets
💡 Factorial Properties
Growth Rate:
- Factorials grow extremely fast
- 10! = 3,628,800
- 20! = 2,432,902,008,176,640,000
Simplification: (n!)/((n-2)!) = n(n-1)
Calculate factorials with our Factorial Calculator!