You are about to set up your side of the board for a game of chess. Your chesspieces consist of one king, one queen, two bishops, two knights, two rooks, and eight pawns. There are exactly the same number of squares where each piece type can go. (For example, there are two squares where you can place the two knights.)

Since all of the pieces of one type are the same, it does not matter which piece of a type goes in each of the permitted squares, but if it did, how many different possible arrangements would there be for setting up your side of the board?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. **The deadline is Wednesday, November 26, 2014 at noon Pacific Time.** I will post the answer shortly after.