a large number of hydrogen atoms have electrons excited to the n_h=4 state.How many possible spectral lines can appear in the emission spectrum as a results of the electron reaching the ground state(n_1=1)?

Answer 1

I count 6.
4 to 1
4 to 2
4 to 3
3 to 2
3 to 1
2 to 1
You might want to draw out the levels and make sure that's all.

Answer 2

200