Answer
Free radical halogenation produces a mixture of products because the hydrogens are substituted by halogen atoms, which may occur in any combination.
Work Step by Step
When a halogen atom substitutes a hydrogen, even if the molecule has only one type of hydrogen, it's substitution creates a new compound. This new compound may have more hydrogen atoms which compete with the initial reactant for substitution via halogen atoms. So, for example, chlorination of methane produces a mixture of products such as $CH_3Cl, CH_2Cl_2, CHCl_3, CCl_4$.
And if a compound has different types of hydrogen, a mixture of products is obtained.
