Hi everyone.

Lately I've done some combinatorial problems. And I am wondering.
What methods are used to calculate the binomial coefficients?
What is the most effective?

I have used dynamic programming, although it is effective for many
queries and can be modulated with any number, the range is too limited.


When the number is a bit higher, I have used modular arithmetic
but I need to precalculate all factorials and is needed a prime number
as a module and really the range is not so large just 10 ^ 5 maybe.
If the problem have higher numbers, I'm lost

Can you tell me what techniques you use and when they can be used are?
I hope you can help me
Thank you