It's a branch of pure math concerning the study of decrete objects
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Combinatorics is a part of math focused on counting principles of finite quantities. It does not really have much to do with triangles, much less the Pythagorean theorem.
Hindu studies of combinatorics but Pascal discoevered more uses for it. If you add up the diagonals of Pascal's triangle, the sums are the entries of the Fibonacci Sequence.
Algebra is a branch of mathematics concerning the study of structures, relation and quantity. Together with geometry, analysis, combinatorics and number theory, Algebra is one of the main branches of mathematics.
It really depends on fields. In my view the 3 most important math fields that are important in computer science are: Discrete maths - Set theory, logic, combinatorics Number theory - Vital in cryptography and security. Geometry and Matrices - Game theory etc.
15/21= 71.43% chance. It's the number of possible throws without repetition divided by the total different combinations of dice throw. Here is a handy Combination and Permutation Calculator: http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html