N1994 P1 Q13

A panel of judges in an essay competition has to select, and place in order of merit,\(4\) winning entries from a total entry of \(20\). Find the number of ways in which this can be done.

As a first step in the selection, \(5\) finalists are selected, without being placed in order. Find the number of ways in which this can be done.

All \(20\) essays are subsequently assessed by three panels of judges for content, accuracy and style, respectively, and three special prizes are awarded, one by each panel. Find the number of ways in which this can be done, assuming that an essay may win more than one prize.