# 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

https://brainmass.com/math/probability/probability-based-order-random-selection-15603

#### 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.