Question

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?

Answer 1

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