Chris wants to put six plants in a row on his windowsill. He randomly chooses each plant to be an aloe plant, a basil plant, or a violet. What is the probability that either exactly four of the plants are aloe plants or exactly five of the plants are basil plants?
Can Chris have four AND five plants? No. So we have to use casework to try to find out what the probability for having 4 aloe plants or 5 basil plants. Long story short, the math ends up as 24/243 = 8/81.
