Final answer:
Using the Pigeonhole Principle, one must take 6 candies to be sure of getting at least one candy of the same color, as there are 5 different colors of candies in the box.
Step-by-step explanation:
The question is asking for the application of the Pigeonhole Principle in a probability and combinations context. To be sure you have at least one candy of the same color, you must take out more candies than there are different colors since if you take one of each color, the next one you take will definitely be a repeat color.
In this case, there are 5 colors: black, white, green, blue, and yellow. If you take one of each color, you would have 5 candies. Therefore, to be sure that you have at least one candy of the same color, you would need to take out 6 candies.