6.21Loops_MultiplyAndDivideFactorials

using System;
using System.Numerics;
class MultiplyAndDivideFactorials
{
    static void Main ()
    {
        checked
        {
            Console.Write("Please, enter a whole number, bigger from 1 for N = ");
            string numberStr = Console.ReadLine();
            int numN = int.Parse(numberStr);
            Console.Write("Enter other whole number, bigger from N for K = ");
            numberStr = Console.ReadLine();
            int numK = int.Parse(numberStr);
            if (numK <= 1 || numN >= numK || numN < 1)
            {
                Console.WriteLine("Error - Invalid Input !!!");
            }
            else
            {
                /* If looked deeply in factorial function formula, we will understand
                 * why is not necessarily calculate N! and K! separately.
                 * N!=N*(N-1)*(N-2)*...*1 and K!=K*(K-1)*(K-2)*...1;                 *
                 * If K>N, the factorial of (K-N)! is Subset of K!,
                 * that's mean: K!=K*(K-1)*(K-2)*...*(K-N+1)*(K-N)!;
                 * From all of this follows, to calculate Result from (N!*K!)/(K-N)!,
                 * must calculate only multiplication of two expessions:
                 * 1) Factorial of (K-N+1)*(K-N+2)*...*(K-1)*K;
                 * 2) Factorial of N!
                 * Result = 1) * 2)
                 * Example: If N=4, K=7, 1)=840, 2)=24, Result=20160  */

                BigInteger factorialKToKminusNplus1 = 1;
                for (int i = numK; i > (numK - numN); i--)
                {
                    factorialKToKminusNplus1 *= i;
                }

                BigInteger factorialN = 1;
                for (int j = 1; j <= numN; j++)
                {
                    factorialN *= j;
                }

                BigInteger multiplicationResult = factorialKToKminusNplus1 * factorialN;
                Console.WriteLine("The Result of Multiplication and Division of these factorials is:");
                Console.WriteLine("RESULT = {0} !", multiplicationResult);
            }
            Console.ReadLine();
        }
    }
}