How to calculate efficient binominal coefficient or sum of these coeficients mod value?

Question

The task is to write a program, what would calculate the large binominal coefficient: n!/m!/(n-m)! mod value efficient with a program. As a variant, for the case that this would be simpler, how to calculate sum of sequence of binominal coefficients, like that: C(n/m) + C(n/m-1) ... + C (n/1) where C (n/1) = n obviously, all expression mod value efficient. Any idea, how to solve it please?