SOLUTION: Four people sit around a circular table, and each person will roll a standard sixsided die. What is the probability that no two people sitting next to each other will roll the sam

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Question 116775: Four people sit around a circular table, and each person will roll a standard sixsided die. What is the probability that no two people sitting next to each other will roll the same number after they each roll the die once? Express your answer as a common fraction.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let's number the people clockwise 1,2,3 & 4 and have them roll in order.
1 can roll whatever he wants. His chance at the correct number is 6/6.
2 can roll anything but what 1 rolls. His chance at the correct number is 5/6.
3 can roll anything but what 2 rolls. His chance at the correct number is 5/6.
4 can roll anything but what 1 and 3 roll. They will roll different numbers 5/6 of the time and his chance will be 4/6. 1/6 of the time 1 and 3 will roll the same number and his chance will be 5/6.
We must multiply 4/6 * 5 and add 5/6 =25/6 and then divide by 6 for an average.
25/6*1/6=25/36 probability that 4 will roll anything other than what 1 and 3 rolls.
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(5/6)^3*25/36=3125/7776= .401878... Probability that no two people sitting next to each other will roll the same number after they each roll the die once.
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There is no way to check these problems except by a computer program with a good random number generator, so I hope I'm right.
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Ed