# You hold 10 cards, the Ace through 10 and you lay them randomly down in a row...

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You hold 10 cards, the Ace through 10 and you lay them randomly down in a row.

Now you turn them over one at a time starting with the first. Each time you turn a card face up, that card tells you the position of the card to flip over next. Once it tells you to flip over a card that is already face up, you are done.

What is the probability that you will turn every card face up?

posted Nov 11, 2018

To reach the final card The first card has to be anything but 1: (9/10)
Similarly for the 2nd card (8/9)
Since all the events are to happen one after the other the probabilities are to be multiplied,
(9/10)*(8/9)*(7/8)*(6/7)*(5/6)*(4/5)*(3/4)*(2/3)*(1/2) = 1/10

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