Proof Writing & Problem Solving · Superchallenge problem

One cell is removed from a $5 \times 5$ board, and the remaining $24$ cells are to be tiled by $8$ L-trominoes (each L-tromino is a $2 \times 2$ square with one cell missing, in any of its four orientations). For how many of the $25$ possible choices of the removed cell is a tiling possible?