A person carries 3 bottles of compound X, 3 bottles of compound Y and 3 bottles of compound Z. While X and Y will react vigorously, Z will prevent the reaction from happening. If the person falls and 3 random bottles react, what is the probability that a vigorous reaction will happen?

I tried solving this question like this:

Possible combinations:

ABB

ABA

3/6 x 3/5 x 2/4 = 18/120

3/6 x 3/5 x 2/4 = 18/120

18/120 x 2 = 3/10

I'm wondering if the order of the bottles matter and if the the number of bottles of Z should be counted (e.g. 3/9 x 3/8 x 2/7)?

Please tell me if I'm wrong and provide the right way to do this...