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5 people sitting around a table, what's the probability they're sitting in order of age? Clockwise, anti-clockwise doesn't matter (i.e. can be ascending or descending in age)

Pólya enumeration theorem?actually you dont need that - i got 1/12?

I got that answer aswell, I'm wondering if you did it in a more elegant way than me?Permumtations of 5 is 120, but after that I had to think through the possible ways they can sit in ascending/descending order, which is 10.Is there a more mathematical way to work of the number of positions that satisfies the order age requirement?

your way of counting is already simple enough.i can give you a different reasoning: note the fact that if 3 ppl sit around a table, the probability is 1 that they sit in order of age. if you add another person, he has 3 positions to go, and only one of them would still keep the order, so the probability is 1/3; similarly the 5th person has 4 positions to go, and only one of them keeps the order, so 1/3*1/4=1/12. you can continue to get the probability for n ppl to sit in order is 2/(n-1)!.this does not really give more insight, since directly counting gives you the same result: 2n/n!, or if you are familiar with circular permutation: 2/(n-1)!http://mathworld.wolfram.com/CircularPermutation.html

QuoteOriginally posted by: wileyswyour way of counting is already simple enough.i can give you a different reasoning: note the fact that if 3 ppl sit around a table, the probability is 1 that they sit in order of age. if you add another person, ....You can also calculate the probability sequentially as you sit people randomly in the five seats. Starting for example with the youngest, he can sit wherever he wants. The next person have four chairs available, and it's ok for him to seat at either side of the previous person. So the probability of getting it right is 1/2. The third person has three choices, and only one chair keeps the order: the probability so far is 1/2*1/3. The fourth person has two choices: 1/2*1/3*1/2. The last person has no chance of getting it wrong, so the final answer is 1/2*1/3*1/2=1/12.