Fundamental Principles and Factorials

Fundamental Principles and Factorials

This lesson covers the following key concepts:

• Fundamental principle of multiplication (product rule)
• Fundamental principle of addition (sum rule)
• Factorial notation and properties
• 0! = 1 and importance
• Simple counting problems
• When to add vs when to multiply

Important Formulas

• $$n! = n \times (n-1) \times (n-2) \times ... \times 2 \times 1$$
• $$0! = 1, 1! = 1$$
• $$n! = n \times (n-1)!$$
• $$\text{Multiplication: if event A in } m \text{ ways, B in } n \text{ ways, both in } m \times n$$
• $$\text{Addition: if event A in } m \text{ ways OR B in } n \text{ ways, either in } m + n$$