Expectations Between Jokers

Probability Level 5

A standard 5252-card deck with nn extra jokers (where n2n\ge 2) is shuffled. Given the expected number of cards between the first joker and the last joker exclusive is a positive integer EE, find the sum of all possible values of EE.

Details and Assumptions

The 5252-card deck with nn extra jokers implies that there are 52+n52+n cards in total.

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