MathDB

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 numbered from

1

15

in clockwise order. Committee rules state that a Martian must occupy chair

1

and an Earthling must occupy chair

15

. 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

N\cdot (5!)^3

. Find

N

Problem Statement