# 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?

##### 1 Answer

Mar 21, 2016

Depending upon the interpretation,

either

or

#### Explanation:

Starting at some seating position the pattern must be:

If different starting locations for this pattern are considered the same seating pattern:

There are

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