IT-CESENATICO 2015 Problem 2

A music streaming service proposes songs classified in $10$ musical genres, so that each song belong to one and only one gender. The songs are played one after the other: the first $17$ are chosen by the user, but starting from the eighteenth the service automatically determines which song to play. Elisabetta has noticed that, if one makes the classification of which genres they appear several times during the last $17$ songs played, the new song always belongs to the genre at the top of the ranking or, in case of same merit, at one of the first genres. Prove that, however, the first $17$ tracks are chosen, from a certain point onwards the songs proposed are all of the same kind.