2. Learning Objectives
• - Understand basic enumeration principles
• - Apply the addition and multiplication rules
• - Recognize and solve problems involving
permutations and combinations
• - Use enumeration strategies in real-world
problems
3. What is Enumeration?
• Enumeration is a way to count the number of
possible outcomes in a situation.
• Common in combinatorics, probability, and
decision-making.
4. Rule 1 - The Addition Rule
• If there are m ways to do A, and n ways to do
B (and A and B are mutually exclusive), then
there are m + n ways to do A or B.
• Example:
• A restaurant offers 3 appetizers or 4 desserts.
Total choices = 3 + 4 = 7
5. Rule 2 - The Multiplication Rule
• If there are m ways to do A and n ways to do
B, then there are m × n ways to do A and B
together.
• Example:
• A password is 2 letters followed by 3 digits:
• 26 × 26 × 10 × 10 × 10 = 676,000
6. Permutations
• Arrangement of objects where order matters.
• Formula:
• P(n, r) = n! / (n - r)!
• Example:
• Arrange 3 out of 5 people: P(5, 3) = 5 × 4 × 3 =
60
7. Combinations
• Selection of objects where order does not
matter.
• Formula:
• C(n, r) = n! / [r!(n - r)!]
• Example:
• Choose 3 students out of 5: C(5, 3) = 10
8. Problem Solving Strategy
• - Understand the question
• - Check if order matters (Permutation vs
Combination)
• - Determine if choices are independent or
exclusive
• - Apply correct rule or formula
• - Simplify and interpret
9. Sample Problem 1 (Addition Rule)
• A student can choose one elective from Art (3
options) or Music (2 options).
• Total = 3 + 2 = 5 electives
10. Sample Problem 2 (Multiplication
Rule)
• A locker code uses 1 letter and 2 digits:
• 26 × 10 × 10 = 2,600 combinations
11. Sample Problem 3 (Permutation)
• How many 4-letter codes from 'MATH'?
• P(4, 4) = 4! = 24
12. Sample Problem 4 (Combination)
• From 10 books, choose 4 to take:
• C(10, 4) = 210
![Combinations
• Selection of objects where order does not
matter.
• Formula:
• C(n, r) = n! / [r!(n - r)!]
• Example:
• Choose 3 students out of 5: C(5, 3) = 10](https://image.slidesharecdn.com/introductiontoenumerationrulesandproblemsolving-250725041341-b6655bd4/85/Introduction_to_Enumeration_Rules_and_Problem_Solving-pptx-7-320.jpg)
