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This question already has an answer here:

Suppose you have a CD of $n$ tracks. Your CD player's shuffle function is broken; it selects a random song, possibly even the one(s) already played, before all tracks are played. How many tracks (possibly duplicates), on average, does one need to listen to to hear every song at least once?

The solution to this problem is $n H(n)$ where $H(n)$ is the n$^\mathrm{th}$ harmonic number.

How is this derived?

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marked as duplicate by Did, user63181, AlexR, Andrew D. Hwang, azimut Mar 15 '14 at 14:57

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    $\begingroup$ This is essentially the same as the coupon collector's problem $\endgroup$ – Mark Bennet Mar 14 '14 at 15:05
  • $\begingroup$ @MarkBennet: I've never heard of that problem. Thanks for letting me know! $\endgroup$ – Geremia Mar 14 '14 at 15:06
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    $\begingroup$ essentially? this IS the coupon collector's problem. Or maybe CD track collector's problem. $\endgroup$ – Guy Mar 14 '14 at 15:08
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This is the coupon collector's problem.

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