Cambridge O Level Additional Mathematics · Syllabus 4037 · Permutations and Combinations
Algebraic Counting Equation
What is Algebraic Counting Equation?
An equation in which the unknown appears inside a permutation or combination expression, such as n C 2 equals 45. It is solved by expanding the expression into a polynomial in n, using the cancelled form of the formula, and then solving that polynomial by ordinary algebra. Because n counts objects it must be a non-negative integer that is at least as large as the lower index, so any algebraic root that is negative, fractional or too small must be rejected explicitly. Stating the rejection is part of the solution, since an answer that lists both roots of the quadratic has not finished the question.
This definition is part of the Permutations and Combinations chapter in Cambridge O Level Additional Mathematics.