A Combinatoric Probability Problem, my program seems to give wrong answer say, I have 3 red balls, 4 yellow balls, 5 blue balls. totally 12 balls
now I randomly arrange the balls, a1...a12
a good layout is such:  a1 = a12 or a1 = a11 or a2 = a12 (= means same color)
what's the probability of gaining a good layout?
I believe it is somewhat 66%=0.2879*3-0.06818*2-0.7273+0.01212 but my program (10000 random runs) gives 44%...
Update
My Maths is correct, my program has a bug..., now corrected.

your simulation program might be wrong. My simulation shows that the probality on 10000 round is 65.6%.
