five pills

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Suppose you are taking one each of 5 different types of pills every day but you donít like having to open and close 5 different bottles, so at the beginning of each (30-day) month you put 30 of each type of pill into one big bottle. When it is time to take your pills, you draw them out of the big bottle one at a time until you have (at least) one of each type. On the last day of the month you will draw exactly 5 pills and they will all be different (because thatís all thatís left in the bottle), but on other days you will generally have to draw more than 5 pills in order to have (at least) one of each type. So, the question is: On the first day of each month (when there are 150 pills in the bottle), how many pills, on average, must you draw from the bottle in order to have (at least) one of each?

Answer


Solutions (listed by author)

Michael A. Gottlieb #1 (pdf, 76K)

Michael A. Gottlieb #2 (Mathematica, 8K)

 

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