Rule 3 is used for goods which can be classified under two or more headings. It's in three separate parts that apply only if the previous rule is eliminated.
Rule 3, part a - two or more headings each referring to part of the materials in composite goods
Rule 3, part a gives directions to which of the two headings your goods could fall under if Rule 2 can't apply. The heading that provides the most specific description of the goods takes precedence over one that provides only a general description. A description by name is more specific than a description by class.
For example shavers and hair clippers are classified in heading 85.10 'shavers and hair clippers and hair removing devices, with self-contained electric motor' not in 84.67 'electro-mechanical tools for working in the hand' or in 85.09 'electro-mechanical domestic appliances with self-contained electric motors'.
Rule 3, part b - mixtures, composite goods of different materials and components, goods put up for sale in sets
Part b relates to the component parts of the goods you're classifying. It states that such goods are to be classified according to the material component that gives them their essential character.
An example of something put up for sale as a set is a hairdressing kit made up of electric hair clippers (heading 85.10), a comb (heading 96.15), a pair of scissors (heading 82.13), a brush (heading 96.03), put up in a leather case (heading 42.02). The clippers are considered to have the essential character, so the whole kit would be classified under heading 85.10.
This rule is used when goods can't be classified using Rule 3 (a).
Rule 3, part (c) - goods unclassifiable by reference to 3 (a) or 3 (b)
Part c comes into play when the goods can't be classified by applying Rule 3 (a) or Rule 3 (b). If there are two or more classification codes that have equal merit, you should apply the heading that, in terms of the numerical order of the Commodity Code, occurs last of them.