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?