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counting and probability intermediate

Problem

Robert likes chocolate milk, so he decides to visit the milk bottling plant every day for a week to get the free samples. Unfortunately for him, the bottling plant sometimes bottles regular milk instead of chocolate milk, so each day the plant has a 2/3 chance of bottling chocolate milk. What is the probability that the bottling plant bottles chocolate milk exactly 4 of the 5 days he visits?
Solution
There are ways to choose which 4 of the 5 days the plant will bottle chocolate milk. For each choice, there is a probability of that on those 4 days they will be bottling chocolate milk and on the other day they will not. Therefore, the total probability on that exactly 4 of the 5 days they will be bottling chocolate milk is .
Final answer
\frac{80}{243}