Fundamental principle of counting — A/L Combined Mathematics

The Fundamental Principle of Counting encompasses two core logical rules that govern combinatorial mathematics: (1) The Multiplication Principle: If an operation can be performed in m distinct ways, and following this a second independent operation can be performed in n distinct ways, the composite sequence of both operations can be executed in m × n distinct ways. This generalizes to k sequential operations: n₁ × n₂ × ... × n_k; (2) The Addition Principle: If two operations are mutually exclusive (cannot occur simultaneously) such that operation A can be performed in m ways and operation B in n ways, then performing either A or B can be completed in m + n distinct ways.

Check before you answer (A/L Pure Maths Paper 1)

1. Multiplication vs Addition Distinction: Accurately determining whether independent successive stages require multiplication or alternative disjoint cases require addition.
2. Repetition Permitted vs Restricted: Applying the multiplication rule with or without repetition (e.g., n^r when digits can repeat versus n(n - 1)... when distinct).
3. Constrained Positions First: Addressing strict constraints first (e.g., units digit must be even for even numbers) before applying multiplication to unconstrained positions.