First, the total number of states is 10, and the number composed of four numbers is 10! /(6! 4! )*4! =5040;

Then calculate the infeasible situation:

Number of cases with odd mantissa: 5*9! /(6! *3! )*3! =2520;

The first digit is "0" and the last digit is even (including odd): 4*8! /(2! *6! )*2! =224;

So the answer is: (5040-224-2520)/5040 = 2296/5040 = 41/90.