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Total number of votes in a Precinct is 350.

The number of democrats is 250

Number of republicans is 100.

Number of voters selected are 30.

30 votes are chosen at random from the precinct.

Therefore, there are\(^{350}{C_{30}}\)ways of selecting 30 voters from 350.

Also, there are\(^{{\bf{250}}}{{\bf{C}}_{{\bf{18}}}}\)ways of selecting 18 democrats.

For selecting exactly 18 democrats, we need to select remaining 12 voters from

100 republicans. Thus, the number of ways to select the 12 voters is \(^{100}{C_{12}}\)

Probability of selecting 18 democrats will be,

\(\begin{aligned}{}\frac{{^{250}{C_{18}}{ \times ^{100}}{C_{12}}}}{{^{350}{C_{30}}}} &= \frac{{\left( {\frac{{250!}}{{18!\left( {250 - 18} \right)!}}} \right)\left( {\frac{{100!}}{{12!\left( {100 - 12} \right)!}}} \right)}}{{\frac{{350!}}{{\left( {350 - 30} \right)!30!}}}}\\ &= 0.0579\end{aligned}\)

Thus, the required probability is 0.0579.