code: import java.math.BigInteger;
  
  public class CombinationsAndPermutations {
  
      public static void main(String[] args) {
          System.out.println(Double.MAX_VALUE);
          System.out.println("A sample of permutations from 1 to 12 with exact Integer arithmetic:");
          for ( int n = 1 ; n <= 12 ; n++ ) {
              int k = n / 2;
              System.out.printf("%d P %d = %s%n", n, k, permutation(n, k));
          }
  
          System.out.println();
          System.out.println("A sample of combinations from 10 to 60 with exact Integer arithmetic:");
          for ( int n = 10 ; n <= 60 ; n += 5 ) {
              int k = n / 2;
              System.out.printf("%d C %d = %s%n", n, k, combination(n, k));
          }
  
          System.out.println();
          System.out.println("A sample of permutations from 5 to 15000 displayed in floating point arithmetic:");
          System.out.printf("%d P %d = %s%n", 5, 2, display(permutation(5, 2), 50));
          for ( int n = 1000 ; n <= 15000 ; n += 1000 ) {
              int k = n / 2;
              System.out.printf("%d P %d = %s%n", n, k, display(permutation(n, k), 50));
          }
  
          System.out.println();
          System.out.println("A sample of combinations from 100 to 1000 displayed in floating point arithmetic:");
          for ( int n = 100 ; n <= 1000 ; n += 100 ) {
              int k = n / 2;
              System.out.printf("%d C %d = %s%n", n, k, display(combination(n, k), 50));
          }
  
      }
  
      private static String display(BigInteger val, int precision) {
          String s = val.toString();
          precision = Math.min(precision, s.length());
          StringBuilder sb = new StringBuilder();
          sb.append(s.substring(0, 1));
          sb.append(".");
          sb.append(s.substring(1, precision));
          sb.append(" * 10^");
          sb.append(s.length()-1);
          return sb.toString();
      }
  
      public static BigInteger combination(int n, int k) {
          //  Select value with smallest intermediate results
          //    combination(n, k) = combination(n, n-k)
          if ( n-k < k ) {
              k = n-k;
          }
          BigInteger result = permutation(n, k);
          while ( k > 0 ) {
              result = result.divide(BigInteger.valueOf(k));
              k--;
          }
          return result;
      }
  
      public static BigInteger permutation(int n, int k) {
          BigInteger result = BigInteger.ONE;
          for ( int i = n ; i >= n-k+1 ; i-- ) {
              result = result.multiply(BigInteger.valueOf(i));
          }
          return result;
      }
  
  }
  