Suppose you have some objects that you want to line up in a row. In how many different ways can you do it? Extensions of the problem and a complete discussion of the underlying mathematical ideas are included.

Suppose you have some objects that you want to line up in a row. In how many different ways can you do it? Extensions of the problem and a complete discussion of the underlying mathematical ideas are included. This mathematically rich problem was originally developed for the Project Discovery Mathematics by Inquiry institutes for middle grades teachers taught in 1992 - 1994 at Ohio State University. Project Discovery was co-funded by the Ohio Board of Regents and the Statewide Systemic Initiative (SSI) program of the National Science Foundation. (author/sw)