Counting

Counting in combinatorics involves determining the number of ways certain arrangements or selections can be made. The two fundamental principles are:

1. Addition Principle: If event $A$ can occur in $m$ ways and event $B$ in $n$ ways, and they cannot both occur together, then there are $m + n$ ways for either $A$ or $B$ to occur.
2. Multiplication Principle: If event $A$ can occur in $m$ ways and, after $A$, event $B$ can occur in $n$ ways, then there are $m \times n$ ways for both $A$ and $B$ to occur in sequence.

Important properties

• Addition and multiplication principles are the foundation of counting.

• Counting can involve arrangements (permutations) or selections (combinations).

• Careful attention is needed to avoid overcounting or undercounting.