In a collection of H-atoms, all the electrons jump from $n=5$ to the ground level (directly or indirectly) without emitting any line in the Balmer series. The number of different possible radiations is:

The correct option is D $6$
Maximum number of spectral lines$\left(N\right)$ corresponding to transition from $n_1=5$ to $n_2=1$ are:
$N=$ number of lines emitted $=\frac{1}{2}(n_1-n_2)(n_1-n_2+1)$
$=\frac{1}{2}(5-1)(5-1+1)$
$=10$
But the emissions in Balmer series aren't taking place. So, the transitions ending at and beginning from $n=2,$ are not possible.
Therefore,$four(5\to 2,4\to 2,3\to 2and2\to 1)$ such transitions aren't possible.
Number of possible transitions $=6$