Permutations and Combinations | Class 11 Mathematics Notes

6.2 Fundamental Principle of Counting

This section introduces the Fundamental Principle of Counting, also known as the multiplication principle. It states that if one event can occur in m ways and a subsequent event can occur in n ways, then the total number of ways both events can occur in sequence is m × n. This principle generalizes to any finite number of successive events, where the total number of outcomes is the product of the number of ways each event can occur. Two illustrative problems are presented: Mohan choosing pants and shirts, and Sabnam choosing school bags, tiffin boxes, and water bottles. The section explains how to count the total number of possible pairs or triplets by multiplying the number of choices at each step. Several examples demonstrate the application of this principle to counting arrangements of letters, flags, and digits with or without repetition. The principle is fundamental to understanding permutations and combinations, as it provides a systematic way to count complex arrangements by breaking them down into simpler successive choices.

📊 Diagram: Fig 6.1; Fig 6.2

🧪 Activity: No specific activity, but examples illustrate the principle.

🔗 Connection: Prepares for formal introduction of permutations, which count ordered arrangements.