Accounting for overlapping "ranges" on a variation on the birthday paradox

Question

So for the birthday paradox, what if you instead wanted to find the probability that any two people in a group of say, five have a birthday *within one day of each other?* When I first thought of this problem I thought you could just calculate it as if there were 15 people in a regular birthday problem since each persons' "range" is triple the size. But if person A has a birthday on 2/1 and person B has a birthday on 2/3, the sum of their "range" extends only five days instead of six. Does anyone know how you could account for this when trying to calculate this?

Answer 1

This problem has been studied . Like for the original problem, you have to compute 1-probab.no.overlap.

The resulting formula is similar. Here is too late , but if nobody answers tomorrow I can copy the formula.