When an electron in a hydrogen atom is excited to $n = 4$, the total number of distinct spectral lines that can appear as it returns to the ground state is

The number of possible transitions between $n$ levels is $\binom{n}{2} = \tfrac{n(n-1)}{2}$. For $n=4$: $\tfrac{4\cdot 3}{2} = 6$. (Option C, 10, is the value for $n=5$.)