If there are only a handful of objects, then you can count them with a moment's thought, but the techniques of combinatorics can extend to quickly and efficiently tabulating astronomical quantities. See more

How many triangles are there in the above image?

\[\large \displaystyle S = \{{1,2,3,\ldots, 19,20}\}\]

How many subsets of three numbers each can be formed from the set above so that no two consecutive numbers are in the set?

**Bonus**: Generalize this for \(n \times n\) grid.

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