First of all 1 in 12 permutations of the Rubik's cube are possible to solve. So only 41 quintillion are possible without taking it apart or moving stickers. Also it takes at most 200 moves to solve so you only see 1/2 quintillion possibilities or 5e-15 (.000000000000005). Thats with the beginners method. If you use the CFOP method (Cross, F2L, OLL, PLL) you can easily do it in under 100 moves. And its not even that hard to learn how to do. It takes 1 hour to do it for the first guidance and 1 week to be able to do it by memory. If you don't have time to learn how to do a 3x3x3 Rubik's cube, you can always do the 2x2x2 rubies cube. It only has 3 algorithms (series of moves[it has more meanings involving computers]) and 1 really short 3 move algorithm.
