Question: (Donated by Dave Perkins) You are captured by an ogre who ties you to a chair at a table and prepares a diabolical puzzle for you. Squatting across from you, the ogre shows you 15 identical chocolate chips and an eyedropper full of sparkling liquid-poisonous sparkling liquid, says the ogre.
(a) Under the table, the ogre drips the liquid onto four of the chips. In how many ways can the ogre arrange the 11 unpoisoned and 4 poisoned chips in a line on the table? It is impossible to tell a poisonous chip from a nonpoisonous one.
(b) The ogre forces you to choose and consume two of the chips. Of the total number of choices, how many will contain at least one poisoned chip?