Every day during the last 10 days, an executive wrote seven letters and his secretary prepared seven envelopes for the letters. The secretary kept envelopes of each day in chronological order in a...

Every day during the last 10 days, an executive wrote seven letters and his secretary prepared seven envelopes for the letters. The secretary kept envelopes of each day in chronological order in a packet, but she forgot to insert the letters in the envelopes. Today, the secretary finds out that all 70 letters and all 10 packets of envelopes are mixed up. If she selects packets of envelopes at random and inserts randomly chosen letters into the envelopes of each packet, what is the approximate probability, obtained by using simulation, that none of the letters is addressed correctly? Note that the envelopes within a packet are left in chronological order but the packets themselves are mixed up. Answer: Approximately 0.53416. For an analytic discussion of this problem, see the article by Steve Fisk in the April 1988 issue of Mathematics Magazine.