# A Particular Domino Tiling

Discrete Mathematics Level 4

A grid with 3 rows and 52 columns is tiled with 78 identical $$2 \times 1$$ dominoes. How many ways can this be done such that exactly two of the dominoes are vertical?

Details and assumptions

• The dominos will cover the entire board. They are not allowed to jut over the board, or overlap with each other.

• Rotations and reflections (of the board) count as distinct ways.

• Convention: Rows are horizontal and columns are vertical.

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