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1 . In the city of ShortLastName, every person has a last name consisting of one uppercase letter, followed by two lowercase letters. No two letters in a last name can be equal. Thus, Lin is a valid last name, whereas Xax is not a valid last name.
What is the minimum size of the population of ShortLastName, such that there must be at least two people who have the same last name?
(a)
$1 + 24 \cdot 25 \cdot 26$
(b)
$1 + 26!$
(c)
$1 + \frac{24 \cdot 25 \cdot 26}{3!}$
(d)
$1 + 26^{3}$