Fundamental Counting Principle Calculator
Choice 1
Result
How to Use
- Enter the number of options for each choice
- Add more choices if needed using the "Add Another Choice" button
- Click "Calculate Total Outcomes" to see the result
- The calculator will show the total number of possible combinations
What is the Fundamental Counting Principle?
The Fundamental Counting Principle states that if there are n ways to do one thing and m ways to do another, then there are n × m ways to do both. This principle can be extended to any number of choices.
Total Outcomes = n₁ × n₂ × n₃ × ... × nₖ
where n₁, n₂, n₃, ..., nₖ are the number of options for each choice
Example
If you have:
- 3 shirt options
- 4 pants options
- 2 shoe options
Total possible outfits = 3 × 4 × 2 = 24 different combinations
Applications
- Probability calculations
- Combinatorics problems
- Decision tree analysis
- Password combinations
- Menu combinations
- Outfit combinations
Common Examples
| Scenario | Choices | Total Outcomes |
|---|---|---|
| Coin Toss | 2 options (Heads/Tails) | 2 |
| Dice Roll | 6 options (1-6) | 6 |
| Two Dice | 6 options × 6 options | 36 |
| Binary Number (3 digits) | 2 options × 2 options × 2 options | 8 |
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