IS THERE ANY CHAIN RULE FOR n choose k PROBLEM

Question

i.e. n1 C k1 * n2 C k2 * n3 C k3 . . . . . . is equal to some other expression

Answer 1

Since each n_i and each k_i can be a different number, your only recourse is to calculate each "nCr" factor separately and then multiply all of them.