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Vahagn Khachatryan
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<h2>Cutting rope</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 398</h3><span style="width:300px;color:#666;">Published on Sunday, 14th October 2012, 08:00 am; Solved by 216</span></div>
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Inside a rope of length <var>n</var>, <var>n</var>-1 points are placed with distance 1 from each other and from the endpoints. Among these points, we choose <var>m</var>-1 points at random and cut the rope at these points to create <var>m</var> segments.
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Let E(<var>n</var>, <var>m</var>) be the expected length of the second-shortest segment.</BR>
For example, E(3, 2) = 2 and E(8, 3) = 16/7.</BR>
Note that if multiple segments have the same shortest length the length of the second-shortest segment is defined as the same as the shortest length.
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Find E(10<sup>7</sup>, 100).</BR>
Give your answer rounded to 5 decimal places behind the decimal point.
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