4 Applied Combinatorics by Alan Tucker is a good one. It's short, not hard to follow, a lot of problems to work through, and it's split into two sections: graph theory in section 1, and combinatorics (generating functions, counting techniques, etc) in section 2.
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A distinctive feature of qualitative methods is the flexibility of research designs, particularly where ethnographic methods using a range of techniques are involved.
A technique is a particular method of doing an activity, usually a method that involves practical skills. ...the techniques of modern agriculture.
- The basic method for making or doing something, such as an artistic work or scientific procedure: learned the techniques involved in painting murals. 2. Skill or command in a particular activity: a pianist with superb technique. See Synonyms at skill.
technique (countable and uncountable, plural techniques) (uncountable) The practical aspects of a given art, occupation etc.; formal requirements. [from 19th c.]
Techniques definition: Plural form of technique; various methods or skills used to achieve a specific goal. - See meaning, pronunciation, etymology, examples, and related words.
So if "combinatorics is a subset of discrete mathematics" should indeed be true: I would like to see a concrete example of a subject being discrete math, but not combinatorics. I was a bit surprised to find that the (oldschool?) viewpoint "combinatorics = counting" is also suggested by our MSE tag descriptions.
In fact,I once tried to define combinatorics in one sentence on Math Overflow this way and was vilified for omitting infinite combinatorics. I personally don't consider this kind of mathematics to be combinatorics, but set theory. It's a good illustration of what the problems attempting to define combinatorial analysis are.