Fundamental Principle of Counting

Subtitle: Data Science and A.I. Lecture Series

Fundamental Principle of Counting

• Statement: If one event can occur in m ways and another event can occur in n ways, then the two events together can occur in m × n ways.
• This principle can be extended to multiple events. For example:Total ways for 3 events = m × n × p
• The principle is widely used in problems involving arrangements and selections.

Example 1: Mohan’s Pants and Shirts

• Mohan has 3 pants (P₁, P₂, P₃) and 2 shirts (S₁, S₂).
• For each pant, there are 2 choices of shirts.
• Total combinations:3 × 2 = 6
• The combinations are:P₁S₁, P₁S₂, P₂S₁, P₂S₂, P₃S₁, P₃S₂

Diagram for Pants and Shirts

Example 2: Sabnam’s School Supplies

• Sabnam has:
  • 2 school bags (B₁, B₂),
  • 3 tiffin boxes (T₁, T₂, T₃),
  • 2 water bottles (W₁, W₂).
• For each school bag, there are 3 choices of tiffin boxes.
• For each pair of school bag and tiffin box, there are 2 choices of water bottles.
• Total combinations:2 × 3 × 2 = 12

Example 3: 4-Letter Words from “ROSE”

• To form 4-letter words with “ROSE” (no repetition):
  • First letter: 4 choices,
  • Second letter: 3 choices,
  • Third letter: 2 choices,
  • Fourth letter: 1 choice.
• Total words:4 × 3 × 2 × 1 = 24

Example 4: Signals with Flags

• If 4 flags of different colors are available:
  • First flag: 4 choices,
  • Second flag: 3 choices (no repetition).
• Total signals:4 × 3 = 12

PDF Presentation

Principle of Counting

Video

 

Fundamental Principle of Counting Quiz

1. How many combinations are there for Mohan's pants and shirts?

3
6
9

2. How many combinations are there for Sabnam's school supplies?

12
6
18

3. How many 4-letter words can be formed from "ROSE"?

12
18
24

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