Practice By Tag: The Pigeonhole Principle
Question: 2015 Fall Midterm - 71 .
$\newcommand{\ShortLastName}{{\rm S {\scriptsize HORT} L {\scriptsize AST} N {\scriptsize AME}}}$
In the city of $\ShortLastName$, every person has a last name consisting of two characters, the first one being
an uppercase letter and the second one being a lowercase letter. What is the minimum number of people
needed so that we can guarantee that at least 4 of them have the same last name?
(a)
$3 \cdot 26^{2}$
(b)
$4 \cdot 26^{2}$
(c)
$4 \cdot 26^{2} + 1$
(d)
$3 \cdot 26^{2} + 1$