Shuffling And Deleting

Discrete Mathematics Level 2

We begin with the set \( \{ 1, 2, 3, \ldots , 2016 \} \).

We will perform the following operations on the set until the set has only one element left:

  1. Shuffle the set.
  2. Delete the first element.

The probability that the last remaining element is 2016 can be written as \( \dfrac AB\), where \( A \) and \(B\) are positive coprime integers. Find \(A + B\).

Note: After shuffling a set of \(n\) distinct elements, any of the \(n!\) permutations is equally likely to occur.


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