2. (12 points) Thirty-six people have been invited to a party. Each invitee meets all other invitees individually, and a single picture is taken during the short conversation between each two guests. (a) Showing your work, determine the total number of pictures taken. (b) If 12 invitees are from out of state and others are local, what is the probability (in four decimal places) of randomly selecting two invitees and those two are not local? Show your work