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**Plato** Use the following notation $\mathcal{T}$ is the set of those numbers **starting with three**; $\mathcal{F}$ is the set of those numbers having **middle digit five**; $\mathcal{S}$ is the set of those numbers having **last digit seven**.

The notation $\|\mathcal{A}\|$ is the number of terms in the set $\mathcal{A}$.

This question is asking for $\|\mathcal{T\cup F\cup S}\|$ which means that you must know the *inclusion/exclusion* rules.

$\|\mathcal{T\cup F\cup S}\|=\|\mathcal{T}\|+\|\mathcal{ F}\|+\|\mathcal{ S}\|-\|\mathcal{T\cap F}\|-\|\mathcal{T\cap S}\|-\|\mathcal{ F\cap S}\|+\|\mathcal{T\cap F\cap S}\|$

Here is a start $\|\mathcal{F}\|=(9)(10)^3$ & $\|\mathcal{T\cap S}\|=(10)^3$