AIME I 2009 #10

[stupidityismygam]

The Annual Interplanetary Mathematics Examination (AIME) is written by a committee of five Martians, five Venusians, and five Earthlings. At meetings, committee members sit at a round table with chairs numbers from [unparseable or potentially dangerous latex formula] to [unparseable or potentially dangerous latex formula] in clockwise order. Committee rules state that a Martian must occupy chair [unparseable or potentially dangerous latex formula] and an Earthling must occupy chair [unparseable or potentially dangerous latex formula] Furthermore, no Earthling can sit immediately to the left of a Martian, no Martian can sit immediately to the left of a Venusian, and no Venusian can sit immediately to the left of an Earthling. The number of possible seating arrangements for the committee is [unparseable or potentially dangerous latex formula] Find [unparseable or potentially dangerous latex formula]