This was a problem proposed some years ago by Professor Forbes, when discussing the question of the distribution of the stars. Simple as it is, no prior notice seems to have been taken of it, nor is the author aware that the full solution has yet been given. The problem is this:—“There are n dice, each of which has p faces, p being not less than n; it is required to find the number of arrangements which can be formed with them; 1st, “that no two shall show the same face; 2d, that no three shall show the same face, and so on.” The only part of this problem of which the solution has yet appeared is the first, and the result is p (p−1). … (p−n+1). The author supplies the solution of the remaining portions.