The following method of solving a certain type of problem in permutations and combinations, and in probability, is so simple that it must have been used before. On the other hand, the writer has never seen it expounded in the following form, and it does not seem to be well known to students. Whilst, therefore, no originality is claimed, this note may be found of interest to readers; and they may care to compare the length of the solutions to the examples below with those to be found in the text-books employing more conventional methods.