Factorial Probability Calculator

Real-time computations for permutations, combinations, and probability calculations

Factorial Probability Calculator

Items
Enter the total number of items (max 170 due to computational limits)
Items
Enter the number of items selected (must be ≤ n)
Outcomes
Enter favorable outcomes for probability calculation (must be ≤ r)
Calculation Steps
Enter values and click "Calculate All" to see detailed steps here.

Calculation Results

Factorial (n!)
3,628,800
Permutations P(n,r)
720
Combinations C(n,r)
120
Probability
0.3
Permutations with Repetition
1,000
n^r = 10^3
Combinations with Repetition
220
C(n+r-1, r) = C(12, 3)

Additional Features

Enter a value to calculate its factorial
Enter a value to calculate its double factorial
For large n: √(2πn) * (n/e)^n
log(n!) for large factorials

How to Use the Factorial Probability Calculator

Understanding Factorials in Probability

Factorials are fundamental to probability and combinatorics. The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

In probability theory, factorials are used to calculate permutations and combinations, which are essential for determining the number of possible arrangements or selections of items.

Key Features of This Calculator

  • Real-time Calculations: Results update instantly as you change input values
  • Multiple Calculations: Compute factorials, permutations, combinations, and probabilities simultaneously
  • Step-by-Step Breakdown: See detailed calculation steps for better understanding
  • Advanced Functions: Calculate double factorials, Stirling's approximation, and log factorials
  • Calculation History: Access previous calculations with the history feature
  • Copy Results: Easily copy any result to clipboard with one click

Step-by-Step Guide

  1. Enter Total Items (n): Input the total number of items in your set (e.g., number of balls in a bag, cards in a deck).
  2. Enter Selected Items (r): Specify how many items you're selecting or arranging from the total.
  3. Enter Favorable Outcomes (k): For probability calculations, enter the number of favorable outcomes.
  4. Click Calculate: Press the "Calculate All" button to compute all factorial-based probabilities.
  5. Review Results: Check the results panel for factorial value, permutations, combinations, and probability.
  6. Use Advanced Features: Try the additional calculators for specific factorial calculations and approximations.

Practical Applications

Lottery Odds: Calculate your chances of winning by determining the number of possible combinations.

Card Games: Determine probabilities of drawing specific hands in poker or other card games.

Genetic Combinations: Calculate possible genetic variations in biology and genetics research.

Password Security: Estimate the strength of passwords based on possible permutations.

Quality Control: Determine sampling probabilities in statistical quality control processes.

Pro Tip

For extremely large numbers where direct factorial calculation is impossible, use Stirling's Approximation or the Logarithm of Factorial feature to get approximate values. This is particularly useful in statistical mechanics and large-scale probability calculations.