A solution of sodium chloride is mixed with a solution of lead(II) nitrate. A precipitate of lead(II) chloride results, leaving a solution of sodium nitrate. Into which class(es) does this reaction fit?

Double displacement reaction

Explanation:

The chemical reaction is as follows :

NaCl + Pb(NO3)2 → PbCl + NaNO3.

Balanced equation:

Pb(NO3)2 + 2NaCl → PbCl2 + 2NaNO3

The reaction is a double displacement reaction . A double displacement reaction is a chemical reaction between compound where the cations and the anions of the 2 reactants exchange places to form a new product.

Double displacement reaction, the 2 reactants exchange ions to form new compounds. Double displacement reaction usually produce a solid precipitate. A good illustration of a double displacement reaction is

AB + CD → AD + CB.

From the reaction above the Sodium ion replace lead to from sodium nitrate while lead replace sodium to form the precipitate lead chloride.  The anions(negatively charged ions) also exchange position.  

the answer is definitely c.