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Probability Based on Order and Random Selection

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

Solution Preview

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 ...

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.