Category:Fundamental Principle of Counting

This category contains pages concerning Fundamental Principle of Counting:

Let $A$ be a finite set.

Let $\sequence {B_n}$ be a sequence of distinct finite subsets of $A$ which form a partition of $A$.

Let $p_k = \size {B_k}$ for each $k \in \closedint 1 n$.

Then:

$\ds \size A = \sum_{k \mathop = 1}^n p_k$

That is, the sum of the numbers of elements in the subsets of a partition of a set is equal to the total number of elements in the set.