Please help me solve this problem. I need to show my work and I'm not even sure where to start. Thanks in advance.

A gum ball dispenser has 38 orange gum balls. 30 purple ones and 18 yellow ones. Using three quarters what is the probability that of the 3 gum balls obtained, exactly 1 will be purple and one will be yellow?

There are 86 gumballs in all. The probability of getting a purple is 30/86. The prob. Of a yellow is then 18/85. The other one has to be orange, so 38/84

But these can come out in 3!=6 ways.

6(\frac{171}{5117})=\frac{1026}{5117}\approx{0.20}