Yes. Because in you are assuming a blue first, then a green and then a red. Thus the favourable cases are reduced - actually it can be 6 times this.
Favourable cases - <B G R>, <B R G>, <R B G>, <R G B>, <G R B>, <G B R>
Probability of case 1 = 10/60 * 20/ 60 * 30/60
Probability of case 2 = 10/60 * 30/60 * 20/60
...
Probability of case 6 = 20/60 * 10/60 * 30/60
So, required probability = Sum of probabilities of all 6 cases. = 1/6