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The 10 decimal digits, 0,1,2,3,4,5,6,7,8,9 are arranged in a uniformly random permutation. We denote by "a"...

The 10 decimal digits, 0,1,2,3,4,5,6,7,8,9 are arranged in a uniformly random permutation. 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 permutation (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= 86217 and b= 5394. 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 ab is even and X= 0 when that product is odd. Calculate E[X].

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