Compute the probability that a random permutation of the 54 stickers on a Rubik's cube includes no adjacent squares of the same colour by simulation; see https://math.stackexchange.com/questions/4618350.

Question4618350a.java

public class Question4618350a {
    final static int ntrials = 1000000000;
    
    public static void main(String [] args) {
        int count = 0;
        
        outer:
            for (int n = 0;n < ntrials;n++) {
                int [] p = Permutations.getRandomPermutation(54);
                for (int square = 0;square < 6;square++) {
                    for (int x = 0;x < 2;x++)
                        for (int y = 0;y < 3;y++)
                            if (color (p,square,x,y) == color (p,square,x + 1,y))
                                continue outer;
                    for (int x = 0;x < 3;x++)
                        for (int y = 0;y < 2;y++)
                            if (color (p,square,x,y) == color (p,square,x,y + 1))
                                continue outer;
                }

                count++;
            }
        
        System.out.println(count / (double) ntrials);
    }

    static int color (int [] p,int square,int x,int y) {
        return p [9 * square + 3 * y + x] % 6;
    }
}