How many coins? - The Sequel

My nearest doughnut stall sells donuts in packs of 1 1 , 2 2 , or 5 5 . I keep on ordering such doughnut packs uniformly at random until I have a total of more than or equal to 400 400 doughnuts.

If the expected number of 5 5 packs I ordered is n n , what is the value of 10 n \left\lfloor 10n\right\rfloor ?

Thanks to @bobbym none for checking the answers


The answer is 501.

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