# Probability Based on Order and Random Selection

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Four couples, each consisting of one man and one woman, are seated at a circular table. Assuming that each different order is equally likely, find the probability that:

a) Andrew is sitting next to his partner

b) Benjamin, Charles and David are sitting together (in any order)

c) The men and women sit alternately

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##### Solution Summary

Probability based on order and random selection are calculated. Combinations and permutations are used. The solution will best suit students who already have a good understanding of combination and permutation equations.

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Solution. The total possible assignments for their seats is (8-1)!=7!

(1) If Andrew is sitting next to his partner

We can think about Andrew couple as a person, then there are (7-1)!=6! possible cases. But they can change their seats, so the total possible case where Andrew is ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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