Question 25
The diagram below shows a $2\times5$ board with 7 unit cells coloured gray. In how many ways can one fill the numbers 1, 2, 3, 4, 5, 6 and 7 into the gray cells, where each cell can be filled with exactly one number, and each number is used exactly once, such that the numbers on the first row are increasing from left to right and the numbers on the second column and on the fourth column are increasing from top to bottom?
