CAYLEY 2015 Problem 24

In the diagram, a rectangular ceiling PQRS measures 6\:m by 4\:m and is to be completely covered using 12 rectangular tiles, each measuring 1\:m by 2\:m. If there is a beam, TU, that is positioned so that PT=SU=2\:m and that cannot be crossed by any tile.

Image

The number of possible arrangements of tiles is

Answer Choices
A. 180
B. 190
C. 185
D. 170
E. 175