Counting the possible orderings of distinct elements [a,b,c,d,e,f] given that a < d, b < e, c < b, c < f, d < f, d < e.

gistfile1.txt

from itertools import permutations

perms = permutations(range(6))

def check(p):
    i1 = p.index(0) < p.index(3)
    i2 = p.index(1) < p.index(4)
    i3 = p.index(2) < p.index(1)
    i4 = p.index(2) < p.index(5)
    i5 = p.index(3) < p.index(4)
    i6 = p.index(3) < p.index(5)
    return i1 and i2 and i3 and i4 and i5 and i6

print len(filter(check, perms))