Battleship and Configuration probabilities

1. Nov 20, 2009

cecih

Hi All,

I'm doing a study that looks at how children think probabilistically while playing battleship. I'm trying to figure out the probabilities of the different configurations of the ships that can exist. So for those that don't know battleship--there is a 10 x 10 grid and you have to hide 5 ships ( one of length 5, 1 of length 4, 2 of length 3, and 1 of length 2). The ships can traditionally only be placed horizontally or vertically. This leads to the following possible configurations: all 5 ships being placed horizontally, 4 ships being placed horizontally and 1 vertically, 3 ships being placed horizontally and 2 vertically, 2 ships being placed horizontally and 3 vertically, 1 ship being placed horizontally and 4 vertically, and all ships being placed vertically. Its been a while since I've done this type of math--so I'm at a bit of a loss as to where to start--and the variation in ship size as well as space constraints are throwing me off as well--any suggestions on how to approach this problem?