A college of 20,000 students provides each student with an Internet account. Explain why letting each student each student have his or her initials as the username cannot possibly work. Assume that each person has a first name, middle name, and last name and therefore that each person's initials consists of three letters.

Explain using permutation. How would I do this?

I said that each student having his or hers intials may not work because combinations can repeat as it is very likely that people have the same starting letter for their first name and possibly additionally their last name.