9*9 矩阵U（R,S）问题

太阳之诚

小弟现有一题，想了很久也无果。只好请教高手的指点！

背景描述看图片，有两个问题待求解。

Question 1：Find out how many 9x9 binary matrices exist with a row sum of (1, 6, 5, 5, 4, 4, 4, 3, 9) and column sum of (6, 5, 3, 6, 6, 2, 2, 6, 5).

Question 2：For all the matrices you found in Question 1, how many of them also have a sum of (1, 1, 1, 2, 3, 4, 1, 3, 4, 5, 5, 2, 2, 2, 2, 2, 1) along the 45 degree diagonal?

多谢各位指点！