How many ways are there for 5 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall? Pick.
A) 6  B) 12  C) 240  D) 100  E) 720
So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 5 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 5! different ways, so total 2*5!=240.   Answer 240.
<result>C</result>
How many ways are there for 5 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?