How many ways can you seat #5# gentlemen and #3# ladies around a circular table with the requirement that every gentleman is seated next to at least one lady?
Depending upon the interpretation,
Starting at some seating position the pattern must be:
If different starting locations for this pattern are considered the same seating pattern:
and for each of these, there are
for a total of
If the starting location for this pattern is considered to give a different way of seating then
there will be