https://gall.dcinside.com/m/github/7529 Solution(C++17)

main.cpp

#include <iostream>

template<unsigned int N>
constexpr unsigned int factorial_v = N * factorial_v<N - 1>;

template<>
constexpr unsigned int factorial_v<1> = 1;

template<unsigned int N, unsigned int K>
constexpr unsigned int binomial_v = factorial_v<N> / (factorial_v<K> * factorial_v<N - K>);

template<unsigned int... Ks>
constexpr unsigned int multinomial_v = factorial_v<(Ks + ...)> / (factorial_v<Ks> * ...);

int main() {
    std::cout << factorial_v<5> << std::endl; // 120
    std::cout << binomial_v<5, 2> << std::endl; // 10
    std::cout << multinomial_v<5> << std::endl; // 1
    std::cout << multinomial_v<3, 2> << std::endl; // 10
    std::cout << multinomial_v<2, 2, 2> << std::endl; // 90
    return 0;
}