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Tue 31 Mar, 2015 01:18 am
A deck of 52 cards labeled 1 to 52 is shuffled at random. You do the follow steps:
1) Reveal the first card on the top of the deck and,
2) Shout the number '1'
Then you repeat the steps above, with the number shouted increases by 1 each time, until all cards are revealed.
What is the probability of at least having one card with a number label that matches the number shouted?
What if there is a deck with infinte cards instead of 52 cards?
@thegiant,
Hint: it will simplify the problem conceptually if you focus on finding the probability that NO label matches the number shouted.
@thegiant,
Look up "Derangement" at wikipedia and go the "Counting derangements" section.