Binomial coefficients in the context of "Gerolamo Cardano"

In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written ${\displaystyle {\tbinom {n}{k}}.}$ It is the coefficient of the x term in the polynomial expansion of the binomial power (1 + x); this coefficient can be computed by the multiplicative formula

$${\displaystyle {\binom {n}{k}}={\frac {n\times (n-1)\times \cdots \times (n-k+1)}{k\times (k-1)\times \cdots \times 1}},}$$