COMBINATORICS is the study that counts the decisions available to us in a DEMOCRACY and MARKET-ECONOMY as citizen-consumers. The failure of "merit testing" (supposed to make "equal opportunity" needless!) to include COMBINATORIC PROBLEMS makes this testing a MOCKERY!

(Elsewhere, I've a combinatorial mathtivity for children, "How to build a googol world in a shoebox".)

This third of the MATH DNA, combinatorics has been called "counting without counting", since it provides simple formulas for computing the choices without having to count them. Unfortunately, except for permutations (explained below), combinatorics is not taught outside of a rare college course, and is ignored by I.Q. and S.A.T. testing!

Euler also discovered a combinatorial formula which is one of the most powerful tools of TOPOLOGY.

The fourth DNA COMPONENT is GROUP THEORY.