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Suppose there are 666 coins with 6 different colors in a non-transparent box. 111 of them are white coins. 111 of them are black coins. 111 of them are yellow coins. 111 of them are red coins. 111 of them are green coins. 111 of them are blue coins. You are going to repeatedly randomly take out one coin from the box, record its color and put it back to the original box. Assume that each time after you put the previous coin back and before you take out one coin, all 666 coins in the box have been “shuffled” thoroughly and all coins are the same in any other physical attributes except for their colors.

What is the expected number of coins needed until you have seen all types of coins?

I've been stuck on this question for hours, can someone explain it?

joriki
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Sakeeb Hossain
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    You would get the same answer with a box of $6$ coins each a different colour, if you are sampling with replacement. A coupon collector's problem – Henry Dec 17 '15 at 19:02
  • This is the Coupon Collector Problem https://en.wikipedia.org/wiki/Coupon_collector%27s_problem – lulu Dec 17 '15 at 19:02

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