explain the "70"

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