15 Slugger Bubble Gum Company markets its best-selling brand to young baseball fans by including pictures of current baseball stars in packages of its bubble gum. In the latest series, there are 20 players included, but there is no way of telling which player's picture is inside until the package of gum is purchased and opened. If a young fan wishes to collect all 20 pictures, how many packages must he buy, on average? Assume that there is no trading of one player's picture for another and that the number of cards printed for each player is the same.