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Question 5 A standard poker deck contains 52 cards. A perfect shuffle consists of taking the top 26 into your left hand, the bottom 26 into your right hand, and then interleaving them so that the top card from your left hand is on top, then the top card from your right, then the next from your left, etc. Number the cards 1 to 52, starting at the top of the deck, and think of a perfect shuffle as a permutation. 1. Write this permutation as a product of disjoint cycles. 2. Find the order of this permutation. 3. What is the real world implication of this fact?

Question 5 A standard poker deck contains 52 cards. A perfect shuffle consists of taking the top 26 into your left hand, the bottom 26 into your right hand, and then interleaving them so that the top card from your left hand is on top, then the top card from your right, then the next from your left, etc. Number the cards 1 to 52, starting at the top of the deck, and think of a perfect shuffle as a permutation. 1. Write this permutation as a product of disjoint cycles. 2. Find the order of this permutation. 3. What is the real world implication of this fact?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question 5 A standard poker deck contains 52 cards. A perfect shuffle consists of taking the top 26 into your left hand, the bottom 26 into your right hand, and then interleaving them so that the top card from your left hand is on top, then the top card from your right, then the next from your left, etc. Number the cards 1 to 52, starting at the top of the deck, and think of a perfect shuffle as a permutation. 1. Write this permutation as a product of disjoint cycles. 2. Find the order of this permutation. 3. What is the real world implication of this fact?
Transcribed Image Text:Question 5 A standard poker deck contains 52 cards. A perfect shuffle consists of taking the top 26 into your left hand, the bottom 26 into your right hand, and then interleaving them so that the top card from your left hand is on top, then the top card from your right, then the next from your left, etc. Number the cards 1 to 52, starting at the top of the deck, and think of a perfect shuffle as a permutation. 1. Write this permutation as a product of disjoint cycles. 2. Find the order of this permutation. 3. What is the real world implication of this fact?
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