Order Santa's Reindeer
It is a foggy night, so Santa needs Rudolph the red-nose reindeer to lead the pack. He has another 8 reindeer, namely Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner, Blitzen. He wants to attach them to his sleigh in \(4\) rows of \(2\) reindeer each. Assuming ordering among each row does not affect the number of ways to order the reindeer, let the number of orderings be \(N\). Find the last three digits of \(N\).