Problem 398
Cutting rope
Inside a rope of length n, n-1 points are placed with distance 1 from each other and from the endpoints. Among these points, we choose m-1 points at random and cut the rope at these points to create m segments.
Let E(n, m) be the expected length of the second-shortest segment.
For example, E(3, 2) = 2 and E(8, 3) = 16/7.
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.
Find E(107, 100).
Give your answer rounded to 5 decimal places behind the decimal point.
割绳子
在一条长为n的绳子上，分布有间距（及最外侧与绳子末端距离）为1的n-1个点。在这些点中，我们随机选择m-1个点，并在这些点处切开，使绳子分成m个分段。
记E(n, m)为第二短的分段的期望长度。
例如，E(3, 2) = 2以及E(8, 3) = 16/7。
注意如果有多个分段均为最短长度，那么第二短的分段长度即为最短长度。
求E(107, 100)。
将你的答案四舍五入到小数点后5位小数。