2015 Countdown Problem #3: An A-maze-ing Maze

An ant wishes to travel from point A to point B along the black lines in the maze shown below. The ant can only either travel upwards and rightwards, and cannot cross any of the grey zones in the maze. Calculate the number of ways the ant can travel between the two points.

Clarification: The ant travels along the black lines and not along the white squares as a whole. After all, it starts and ends at two predetermined points A & B (which aren't squares).

This problem is part of the set 2015 Countdown Problems.

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