I have a 3x3x3 Rubik's Cube. I disassemble it and assemble again in a random way. We've already known that the probability that we can solve it without have to fix any corner or edge is $1/12$. But what is the probability to solve that random assembled Cube:
a. Without have to fix any corner? (So we can fix edge, if necessary)
b. Without have to fix any edge? (So we can fix corner, if necessary)
The factor $1/12$ that a randomly assembled cube is solvable comes from $1/3$ that you do not need to rotate a corner, $1/2$ that you do not need to rotate an edge, and $1/2$ that you do not need to swap the locations of two edges to produce an even permutation. This is described in Wikipedia.