Is there any method to obtain $n \choose k$, for all $n, k \in \mathbb{N}$, using only products of natural numbers without using recursion on binomial coeffcients?
A method that allows one to compute the following binomial coefficients through these operations, for instance: $$ {9 \choose 6} = 2 \cdot 2 \cdot 3 \cdot 7 = 84$$ $$ {10 \choose 4} = 2 \cdot 3 \cdot 5 \cdot 7 = 210$$