# Expectations Between Jokers

Discrete Mathematics Level 4

A standard $$52$$-card deck with $$n$$ extra jokers (where $$n\ge 2$$) is shuffled. Given the expected number of cards between the first joker and the last joker exclusive is a positive integer $$E$$, find the sum of all possible values of $$E$$.

Details and Assumptions

The $$52$$-card deck with $$n$$ extra jokers implies that there are $$52+n$$ cards in total.

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