If I want the expected number of triples (not pairs) out of n people that are have birthdays of within 1 day of each other
$${n \choose 3}*\frac{\text{something}}{365^2} $$
I know that the first bday is given, but how do I count the ways in which the other two can have their bdays fall within the qualified statement. I know I have 3 options for Person 2 but person 3's match depends upon person 2's match.