first of all, think the simplest case, a square:
b a 1 0
d c 2 1
# of a->d = # of a->b + # of a->c
# of ab = 1, # of ac =1, therefore # of ad = 1+1=2
now you can mark the number of paths for each intersection points on your chart, which is :
1 1 1 1 0
5 4 3 2 1
15 10 6 3 1
35 20 10 4 1
70 35 15 5 1
b a 1 0
d c 2 1
# of a->d = # of a->b + # of a->c
# of ab = 1, # of ac =1, therefore # of ad = 1+1=2
now you can mark the number of paths for each intersection points on your chart, which is :
1 1 1 1 0
5 4 3 2 1
15 10 6 3 1
35 20 10 4 1
70 35 15 5 1
