An extremely bored man is sitting on a bench by the elevator on the 15th floor high-rise building ...

 An extremely bored man is sitting on a bench by the elevator on the 15th floor high-rise building, and is trying to guess how many times the elevator will be going down when it opens up, out of the next 20 times it opens on the floor he is on. The elevator operator told him that the probability of the elevator heading down the lower floors on any given time it opens on the 15th floor is about 0.45. Help him out by finding the probability that the elevator is heading down 10 times out of the next 20 times it opens.