Okay, here we have this:
Considering the provided information, we are going to calculate the requested probability, so we obtain the following:
So what we want to know is the probability that three simple events happen, so we will use the formula of favorable cases over possible cases and multiply their results, so we have:
Probability of getting three different colored balls without replacing = Probability of getting the first red ball * Probability of getting the second blue ball * Probability of getting the third yellow ball
Probability of getting three different colored balls without replacing = (Number of Red Balls/Total Balls) * (Number of Blue Balls/Remaining Balls) * (Number of Yellow Balls/Remaining Balls)
Probability of getting three different colored balls without replacing = (4/12) * (2/11) * (6/10)
Probability of getting three different colored balls= (4*2*6)/(12*11*10)
Probability of getting three different colored balls= 48/1320
Probability of getting three different colored balls= 2/55
Finally we obtain that the correct answer is the first option.