The 10 decimal digits, 0,1, 2, 3, 4, 5, 6, 7, 8, 9 are arranged in a uniformly random per- mutation. We denote by x the integer formed in base 10 by the first three positions in this permutation, by y the integer formed in base 10 by the next four positions in this permutation, and by z the integer formed in base 10 by the last three positions in this permutation, (either x or y or z may begin with 0 which is then ignored). For example, if the random permutation is 8620175394 then a = 862, b = 175, and c = 394. Consider the probability space whose outcomes are these random permutations and a random variable X defined on this probability space such X = 1 when the product xyz is even and X = 0 when that product is odd. Calculate E[X].