Permutation and Combination: The Basics of Counting

Key Formulae

• N C R (Combinations):
  • Formula:
  • Commonly used but not the best approach to understand.
• N P R (Permutations):
  • Formula:
  • Also not the best approach to understand.

Core Concept: Counting

Why Counting is Essential

• Understanding counting is crucial for mastering permutations and combinations.
• Counting: Not just basic counting; slightly advanced but easy to grasp.
• Focus on two rules: OR and AND.

Rules of Counting

1. OR (Addition Rule)

   • Example: Picking one item from five distinct items (3 pens and 2 markers).
   • Ways to pick: P1, P2, P3, M1, M2.
   • Total ways to pick one: 3 (pens) + 2 (markers) = 5 ways.
   • OR indicates addition.

2. AND (Multiplication Rule)

   • Example: Picking one pen and one marker from 3 pens and 2 markers.
   • Pairing options: P1M1, P1M2, P2M1, P2M2, P3M1, P3M2.
   • Total ways to pick one pen and one marker: 3 (ways to pick pen) x 2 (ways to pick marker) = 6 ways.
   • AND indicates multiplication.

Practical Example

• Counting circles in a grid.
  • Grid with 6 columns and 4 rows.
  • Total circles: 6 columns x 4 rows = 24 circles.
  • Application of AND rule: Multiplication.

Conclusion

• Mastering permutations and combinations through counting.
• Two Basic Rules: OR (addition) and AND (multiplication).
• Applying these rules simplifies complex problems.
• Watch all tutorial videos to better understand and master the topic.