Consider a variation of the birthday problem: â€œWhat is the

probability that, in a group of n people, at least three have the

same birthday.â€ As with the original birthday problem, for large n

it is not computationally feasible to solve this variation by

setting up and scanning the sample space, nor by using counting

principles. However, this variation can easily be solved using

complement probability. Solve this variation of the birthday

problem using complement probability. A possible answer is given

here:

https://www.chegg.com/homework-help/questions-and-answers/-consider-variation-birthday-problem-probability-group-n-people-least-three-birthday-origi-q25476545?trackid=5a88fe81&strackid=62b06866&ii=3

But i dont understand the answer especially why the part where

exactly 2 people sharing the birthday has the denominator it has.

Thanks