I am trying to get 24 Friends in a Certain Website. I currently have none. $2$ people request to be my friend every day, with an addition of me sometimes sending a friend request which has a chance of happening every day. I also unfriend a person each day, if I hasn't just Friended them or accepted their request that day. Assuming that I'm smart enough to choose the best option every time, what is the probability that I will reach his goal in 12 days? (If he sees a cool friend, I cannot resist friending them, and for the duration of this problem assume that the cool friends always accepts. Also assume that he always has to accept Friend requests, but can Unfriend one each day if he has not just Friended them or accepted their request that day. Also assume that once he reaches his goal, he doesn't have to worry about anything anymore.)