The $$F^-$$ ions make the enamel on teeth much harder by converting hydroxyapatite (the enamel on the surface of teeth) into much harder fluoroapatite having the formula.

Hydroxyapatite, the enamel on teeth, has the formula $$[3(Ca_3(PO_4)_2) \cdot Ca(OH)_2]$$ or $$Ca_{10}(PO_4)_6(OH)_2$$.

When $$F^-$$ ions replace $$OH^-$$, the much harder fluoroapatite is formed according to the reaction:

$$Ca_{10}(PO_4)_6(OH)_2 + 2F^- \rightarrow Ca_{10}(PO_4)_6F_2 + 2OH^-$$

The formula of fluoroapatite is $$[3(Ca_3(PO_4)_2) \cdot CaF_2]$$ or equivalently $$Ca_{10}(PO_4)_6F_2$$.

The correct answer is Option 4: $$[3(Ca_3(PO_4)_2) \cdot CaF_2]$$.