Question

Question:

How many ways may 4 males and 4 females be seated around a circular table if we must have alternating gender (male, female, male, female etc) and two individuals (lets call them Betty and Jim) must not be seated next to each other?

Note: As an additional part to this question you are required to produce a diagram explaining your working or a detailed description as to why your answer is the only answer. Students often have difficulty with these questions, often neglecting to adjust for symmetry or rotations. If you are unsure of your answer try a smaller subset and work up i.e. 2F and 2M then 3F and 3M and see if you can see a pattern in the working (this is how I get students to start to think about the complexity of these problems, with smaller sub problems).

Answer 1

There are 4!ways of sitting the female. However, there are four rotations of the female that do not change their relative order. Thus, there are

4!/4=3!

distinguishable ways of sitting the female. Once they are seated, there are 4! ways of sitting the male. Thus, there are 4!3!=144ways of sitting the female in which the male and femalefalternate seats