Question: 2018 Winter Midterm - 6
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?
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)
$1 + 26^{3}$
(d)
$1 + \frac{24 \cdot 25 \cdot 26}{3!}$