Question: 2014 Winter Final - 18
Consider a group of 5 people. Each person in this group was born in a uniformly random month (from
the 12 months of the year), independent of the other people's month of birth. What is the
probability that at least 2 of these 5 people were born in the same month?
(a)
$1 - \frac{11!}{12^{4} \cdot 8!}$
(b)
$1 - \frac{12!}{12^{4} \cdot 7!}$
(c)
$1 - \frac{11!}{12^{4} \cdot 6!}$
(d)
$1 - \frac{11!}{12^{4} \cdot 7!}$