Lecture on Permutations and Combinations

Introduction

• Combinations (NCR)

  • Formula: ( \frac{N!}{R!(N-R)!} )
  • Commonly taught as a way to select items from a set.

• Permutations (NPR)

  • Formula: ( \frac{N!}{(N-R)!} )
  • Used to arrange items from a set.

• Key Insight: Understanding the formulas alone is not enough to master permutations and combinations.

Importance of Counting

• Counting is the fundamental skill needed to excel in permutations and combinations.
• Advanced counting goes beyond simple finger counting.

Basic Rules of Counting

Rule 1: OR - Addition

• When considering choices as alternatives, use addition.
• Example: Choosing from 3 pens and 2 markers.
  • Choices: P1, P2, P3, M1, M2.
  • Total ways: 3 (pens) + 2 (markers) = 5 ways.

Rule 2: AND - Multiplication

• When considering choices in combination, use multiplication.
• Example: Selecting 1 pen AND 1 marker.
  • Ways to choose a pen: 3.
  • Ways to choose a marker: 2.
  • Total combinations: 3 (pens) x 2 (markers) = 6 ways.
  • Combinations: P1M1, P1M2, P2M1, P2M2, P3M1, P3M2.

Practical Application

• Example: Counting objects in a grid.
  • Observing 6 columns and 4 rows.
  • Total circles: 6 (columns) x 4 (rows) = 24.

Conclusion

• Mastery of permutations and combinations comes from understanding and applying these two basic rules.
• Encouragement to go through additional sessions and videos to fully understand the topic.