Kelvin and $15$ other frogs are in a meeting, for a total of $16$ frogs. During the meeting, each pair of
distinct frogs becomes friends with probability $\frac{1}{2}$ . Kelvin thinks the situation after the meeting is cool
if for each of the $16$ frogs, the number of friends they made during the meeting is a multiple of $4$. Find the probability of the situation being cool.