Tetromino Grid!!

Here is an observation

All the tetro-minoes have to fit neatly inside the grid as the sum of number of squares of tetro-minoes is 20 which is equal to number of squares in the grid.

---

Let's colour each square in the grid alternatively by White and black like a chess board.

So, we'll have an equal number of white and black squares.

---

So, similarly we also have to colour have each square of the tetro-minoes alternatively white and black.

So, we can see that combining all tetro-minoes, we get unequal number of black and white squares.

So, they can't fit neatly in the grid.

So, there are $\boxed{0}$ ways.

Simply, if we take the fourth piece and try to fix it in its possible places then there would be 1 or some squares left near it as the other shapes cannot fit into.

good problem

can be converted into 4 * 4 grid after terminating the tower like piece.

PS : by the way what is it called(the tower like piece)