A conference attended by 200 delegates i...

A conference attended by 200 delegates is held in a hall. The hall has 7 doors, marked A,B,.., G . At each door, an entry book is kept and the delegates enterign through that door sign it in the order in which they enter. If each delegate is free to enter any time and through any door he likes, how many different sets of seven lists would arise in all? (Assume that every person signs only at his first entry).

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