I am a coming freshman. I get a friend who is willing to live me. We are going to request each other as the roommate. However, on the form, we have the same ranking for first and second preferable room, but different ranking for the rest. Do we need to have totally the same ranking of preferences in order to live together for our first and second choices?(If, we get our third preference, we will go with it.) What is the probability to get in your first and second choices? Thank you so much.