Raina places the following balls into a bag. She then draws three balls out of the bag, one at a time, without replacement. What is the probability that the colors of the balls alternate?
There are 3 orange balls and 2 purple balls.
\(\quad\text{Required probability}\\ = \dfrac35 \cdot \dfrac24 \cdot \dfrac23 + \dfrac25 \cdot \dfrac34 \cdot \dfrac13\\ =\dfrac3{10}\)
+1247 
