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# Counting

## Product rule

If a job can be split into two tasks with $$m$$ ways to complete the first an $$n$$ the second, then there are $$m \times n$$ possible approaches

More generaly if there a $$k$$ tasks, with $$n_i$$ ways for completing task $$i$$ then there are $$n_1 \times n_2 \ldots \times n_k$$ ways of completing the job. $\prod_{i=1}^k n_i$

## Sum rule

If a job can either be completed in $$m$$ or $$n$$ ways, then it can be completed in $$m + n$$ ways.

## Subtraction rule

Also: Inclusiion-exclusion principle If a choice can be made between two options, each with $$m$$ or $$n$$ items. The combined possibility are $$m + n -k$$ where $$k$$ is the number of items in common.