# Shuffling And Deleting

Probability 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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