xC3

xC3 is a designation that appears in various contexts. In mathematics, it is most commonly used to denote the binomial coefficient "x choose 3," a function that generalizes the number of ways to select three items from a set of size x. For integer x ≥ 3 it equals x(x−1)(x−2)/6, while for real or complex x it is defined by the gamma-function formula Γ(x+1)/(Γ(4)Γ(x−2)).

In algebra and combinatorics, xC3 appears in expansions such as (1+t)^x via the generalized binomial theorem, and as a polynomial in x: xC3 = (x^3 − 3x^2 + 2x)/6. This makes it useful in counting problems and in deriving closed-form expressions for sums involving consecutive integers.

Other uses: The string xC3 is also employed as a brand name, model identifier, or version tag in software, hardware, or media projects. In such cases the meaning is determined by the issuing organization, and capitalization may vary (examples include XC3 or xC3). Because of its general nature, the intended meaning of xC3 should be inferred from the surrounding context.