1.a how many permutations of the 9 letters a, b,c,d,e, f,g, h, i do not have the

1.a how many permutations of the 9 letters 'a, b,c,d,e, f,g, h, i' do not have the vowels next to each other?
b. how many positive integers less than 1000 consists of distinct digits from {1, 3, 7, 9}.
c. what is the probability that the bit string of length 10 has more 0's than 1's?
d. if r is a relation on {w, x, y, z} where r = {(w,w), (w, x), (x,w), (x, x), (x, z), (y, y), (z, y), (z, z)}, determine whether the binary relation is: (1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.
e. how many permutations of the letters m, n, o, p, q contain the string mn or the string mo or the string op-last year exam?