Suppose you have a playlist with 1000 songs and you set it to play on random. This means that a song will be selected uniformly at random, and when that song completes, another song will be randomly selected and played, etc. By a collision we mean the same song plays twice.

1) Give an expression for the probability that there are no collisions after 5 songs have played.

2) About how many songs will be played before the chance of some collision exceeds 50 percent?