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Pigeonhole Principle: Will 2 people have the same initials?

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Given a group of 680 people, will 2 people have the exact same initials for both their first and last names? Explain the answer.

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Assuming that there are 26 letters in the alphabet (which is the case for the English alphabet) then there are 676 (or 26 x 26) possible combinations of first and last name initials i.e.:

1 2 25 26
1 A with A B with A ....... Y with A Z with A
2 A with B B with B ....... Y with B Z with B
3 A with C B ...

Solution Summary

A step-by-step explanation of the pigeonhole principle with an example.