Applying pigeonhole principle to determine whether a list of strings must have duplicates.

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Say you have a program that creates strings of lower-case letters of length 5 or less. It is told that the program holds 600,000 words on its drive. How can you figure out if all the words are distinct? And the minimal number of words w/o duplicates?

We are told to use the PHP, but I'm not sure how to incorporate it.