A Particular Domino Tiling

Probability Level 5

A grid with 3 rows and 52 columns is tiled with 78 identical 2×12 \times 1 dominoes. How many ways can this be done such that exactly two of the dominoes are vertical?

Details and Assumptions:

  • The dominoes 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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