Mathematics Question from JEE Main 2025 · 2 April, Shift 2

The number of ways, in which the letters A, B, C, D, E can be placed in the $8$ boxes of the figure described below so that no row remains empty and at most one letter can be placed in a box, is:

The figure is a staircase-shaped array of $8$ equal boxes laid out in three rows across four columns: the top row has $3$ boxes (in columns $2$, $3$ and $4$), the middle row has $3$ boxes (in columns $1$, $2$ and $3$), and the bottom row has $2$ boxes (in columns $2$ and $3$).