Approach to shuf?ing a deck of n cards

Reference no: EM131005743

Consider the following approach to shuf?ing a deck of n cards. Starting with any initial ordering of the cards, one of the numbers 1, 2, ... , n is randomly chosen in such a manner that each one is equally likely to be selected. If number i is chosen, then we take the card that is in position i and put it on top of the deck-that is, we put that card in position 1. We then repeatedly perform the same operation. Show that, in the limit, the deck is perfectly shuf?ed in the sense that the resultant ordering is equally likely to be any of the n! possible orderings.

Reference no: EM131005743

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