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 a the integer formed in base 10 by the first five positions in this permutation and by b the integer formed in base 10 by the last five positions in this permuta- tion (either a or b may begin with 0 which in such a case is ignored). For example, if the random permutation is 8621705394 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. Required:

Calculate E[X].