Factorial (n!), Permutation (nPr) and Combination (nCr) Calculator. "Java Code Snippet"

Factorials { n! ~> pronounced n factorial } are used to compute permutations (nPr) and combinations (nCr). A factorial is the result of multiplying a given number of consecutive integers from 1 to the given number. It is written with the exclamation sign: n! and it is defined as
0! = 1
1! = 1
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 = 245! 
5! = 5 x 4 x 3 x 2 x 1 = 120 ...~> and so on   

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Source Code for calculating n!
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   import static java.lang.System.out;
      import java.util.Scanner;

     public class factorial
     {  
           public static void main(String[] args)
           {
                       out.print(" Enter your value : ");

                          Scanner in = new Scanner(System.in);
                             int input = in.nextInt();

                         int fac = 1;
                         for(int num = input; num>=1; num--)
                         {
                     fac = fac * num;
                      }
             
            out.printf(" The factorial of %d = %d" , input, fac);
             out.println();
   }
       }
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Permutation ~> nPr = n!/(n-r)!
In the context of counting problems, Permutations is the arrangements where the order is important and repetitions or recurrence is not allowed. The number of permutations of n distinct points taken r at a time is written as nPr. Because the number of objects is being arranged cannot exceed total number available. There are n! (n factorial) permutations of n symbols. A r-permutation of n symbols is a permutation of r of them. There are n!/(n - r)! different r-permutations of n symbols. A permutations represented by nPr and calculated from the formula nPr = n!/(n - r)!

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Source Code for calculating nPr
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   import static java.lang.System.out;
      import java.util.Scanner;

      public class nPr
      {
                 // static variables n for the value of n and ...
static int n,r, n_Sub_r;

           public static void main(String[] args)
           {
                     out.print(" Enter the value of n = ");

                       Scanner in1 = new Scanner(System.in);
                             int input1 = in1.nextInt();

                             // saving a copy of input1 which is = n
                             n = input1;

                              // calculating n factorial

                              int nFac = 1;

                              for(int num1 = n; num1 >=1; num1--)
                               {
                                nFac = nFac * num1;
        }

                         out.print("\n Enter the value of r = ");

               Scanner in2 = new Scanner(System.in);
               int input2 = in2.nextInt();

                // saving a copy of input2 which is = r
                                             r = input2;

         // calculating the value of n - r as n_Sub_r
                                        n_Sub_r = (n - r);

                         // calculating n - r factorial
                                 int n_rFac = 1;

         for(int num2 = n_Sub_r; num2 >=1; num2--)
         {
          n_rFac = n_rFac * num2;
         }

                         // calculating (n!/(n-r)!)

                             int result = (nFac / n_rFac);

                           out.printf("\n %dP%d = %d\n\n" , n ,r, result);
          }
           }
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Combination~> nCr = n!/(n-r)!r!
Combinations is a method of selecting several items or symbols out of a larger group or a data set, where an order does not matter. The Combination represented by nCr and calculated from the formula nCr = n!/(r!(n - r)!). Each r combination can be arranged in r! different ways. Then the number of r-permutations is equal to the number of r combinations times r!

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Source Code for calculating nCr
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import static java.lang.System.out;
      import java.util.Scanner;

      public class nCr
      {
                 // static variables n for the value of n and ...
static int n,r, n_Sub_r;

           public static void main(String[] args)
           {
                    out.print(" Enter the value of n = ");

                       Scanner in1 = new Scanner(System.in);
                             int input1 = in1.nextInt();

                             // saving a copy of input1 which is = n
                                   n = input1;

                              // calculating n factorial
                                  int nFac = 1;

                              for(int num1 = n; num1 >=1; num1--)
                               {
                                nFac = nFac * num1;
        }

                         out.print("\n Enter the value of r = ");

               Scanner in2 = new Scanner(System.in);
               int input2 = in2.nextInt();

                // saving a copy of input2 which is = r
                                             r = input2;


         // calculating the value of (n - r) as n_Sub_r
                                         n_Sub_r = (n - r);

                                   // calculating n - r factorial
                                         int n_rFac = 1;

         for(int num2 = n_Sub_r; num2 >=1; num2--)
         {
          n_rFac = n_rFac * num2;
         }

                                   // calculating r factorial
     int rFac = 1;

    for(int num3 = r; num3 >=1; num3--)
  {
   rFac = rFac * num3;
  }
                         // calculating (n!/(n-r)!r!)

                         int result = (nFac / (n_rFac * rFac));

                         out.printf("\n %dC%d = %d\n\n" , n ,r, result);
          }
          }
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How to use? Simple; copy and paste code in any IDE of your choice, save, compile then run. GOOD LUCK
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