The color of the phenolphthalein indicator in the basic solution is:

Indicators are the substances that change their color with the change in pH and thus indicate whether the solution is acidic or basic. 

An acidic substance produces hydrogen ions (${\mathrm{H}}^{+}$) in the solution while a basic substance produces hydroxide ions (${\mathrm{OH}}^{-}$) in the solution.

Examples of indicators are phenolphthalein, methyl orange, litmus, and methyl violet.

Now, the phenolphthalein indicator is colorless in acidic solutions and turns pink in basic solutions.  The synthetic indicator phenolphthalein has the chemical formula ${\mathrm{C}}_{20}{\mathrm{H}}_{14}{\mathrm{O}}_4$. It is most frequently employed as an indicator in acid-base titrations and is a member of the phthalein class of dyes. It is dissolved in alcohol for use in studies since it is naturally very poorly soluble in water.

Hence, the color of the phenolphthalein indicator in the basic solution is pink.

Hence, option C is correct.