The formula to calculate the factorial is:

F = n!

Imagine you have a set of five objects in different colors as red, green, blue, white, and black. Imagine you want to arrange the objects in different sequences but you want each sequence to start with two specific objects, for example you may want to arrange the objects so that you always start with any combination of black and white followed by any combination of the other objects. This type of arrangement is called a permutation. The formula to calculate a permutation is:

Imagine you have five objects and you want to arrange the objects in different sequences but you want each sequence to start with certain two objects. This type of arrangement is called a combination. To calculate it, you can use the following formula:

1. Start Microsoft Visual Studio
2. To start a new application, on the main menu, click File -> New Project...
3. In the middle list, click Windows Forms Application and set the Name to Algebra1
4. Click OK
5. On the main menu, click Project -> Add Class...
6. In the middle list of the Add Class dialog box, click C++ Class and click Add
7. Set the Class Name to CAlgebra
    
   
8. Click Finish
9. Change the header file as follows:
   

   #pragma once
   public ref class CAlgebra
   {
   public:
       CAlgebra(void);
   
       long Factorial(long x);
       long Permutation(long n, long r);
       long Combinatorial(long a, long b);
   };

10. Click the Algebra.cpp tab and change the source file as follows:

    #include "StdAfx.h"
    #include "Algebra.h"
    
    CAlgebra::CAlgebra(void)
    {
    }
    
    long CAlgebra::Factorial(long x)
    {
        if( x <= 1 )
    	return 1;
        else
            return x * Factorial(x - 1);
    }
    
    long CAlgebra::Permutation(long n, long r)
    {
        if( r == 0 )
            return 0;
        if( n == 0 )
            return 0;
        if( (r >= 0) && (r <= n) )
            return Factorial(n) / Factorial(n - r);
        else
            return 0;
    }
    
    long CAlgebra::Combinatorial(long a, long b)
    {
        if( a <= 1 )
            return 1;
    
        return Factorial(a) / (Factorial(b) * Factorial(a - b));
    }

11. Display the form
12. Click the body of the form to make sure it is selected.
    In the Containers section of the Toolbox, click TabControl and click the form
13. On the form, right-click the right side of tabPage2 and click Add Page
14. Design the form as follows:
     

    Control Text Name Additional Properties TabControl   tclAlgebra HotTrack: True TabPage Factorial tabFactorial   Label Number:     TextBox   txtFactorialNumber TextAlign: Right Button Calculate btnCalculateFactorial   Label Result:     TextBox   txtFactorial TextAlign: Right

    Control Text Name TabPage Permutation tabPermutation Label n:   TextBox   txtPermutationN Label r:   TextBox   txtPermutationR Button Calculate btnCalculatePermutation Label P(n, r):   TextBox   txtPermutation

    Control Text Name TabPage Combination tabCombination Label n:   TextBox   txtCombinationN Label r:   TextBox   txtCombinationR Button Calculate btnCalculateCombination Label C(n, r):   TextBox   txtCombination

15. Access the Factorial tab page and double-click its Calculate button
16. Implement the event as follows:
    

    #pragma once
    #include "Algebra.h"
    
    namespace Algebra1 {
    
    . . . No Change
     
    System::Void btnCalculateFactorial_Click(System::Object^  sender,
    					 System::EventArgs^  e)
    {
        long result;
        long number = 0;
        CAlgebra ^ statistics = gcnew CAlgebra;
    
        try
        {
            number = long::Parse(txtFactorialNumber->Text);
            result = statistics->Factorial(number);
            txtFactorial->Text = result.ToString();
        }
        catch(FormatException ^)
        {
            MessageBox::Show(L"Invalid Number");
        }
    }
    };
    }

17. Return to the form
18. Access the Permutation tab page and double-click its Calculate button
19. Implement the event as follows:
    

    System::Void btnCalculatePermutation_Click(System::Object^  sender,
    					   System::EventArgs^  e)
    {
        long result;
        long n = 0, r = 0;
        CAlgebra ^ statistics = gcnew CAlgebra;
    
        try
        {
            n = long::Parse(txtPermutationN->Text);
        }
        catch(FormatException ^)
        {
            MessageBox::Show(L"Invalid Number");
        }
    
        try
        {
            r = long::Parse(txtPermutationR->Text);
            result = statistics->Permutation(n, r);
            txtPermutation->Text = result.ToString();
        }
        catch(FormatException ^)
        {
            MessageBox::Show(L"Invalid Number");
        }
    }

20. Return to the form
21. Access the Combination tab page and double-click its Calculate button
22. Implement the event as follows:
    

    System::Void btnCalculateCombination_Click(System::Object^ sender,
    			                   System::EventArgs^  e)
    {
        long result;
        long n = 0, r = 0;
        CAlgebra ^ statistics = gcnew CAlgebra;
    
        try
        {
            n = long::Parse(txtCombinationN->Text);
        }
        catch(FormatException ^)
        {
            MessageBox::Show(L"Invalid Number");
        }
    
        try
        {
            r = long::Parse(txtCombinationR->Text);
            result = Algebra.Combinatorial(n, r);
            txtCombination->Text = result.ToString();
        }
        catch(FormatException ^)
        {
            MessageBox::Show(L"Invalid Number");
        }
    }

23. Return to the form and double-click the Close button
24. Implement the event as follows:
    

    System::Void btnClose_Click(System::Object^  sender,
    			    System::EventArgs^  e)
    {
        Close();
    }

25. Execute the application to test the calculations
     
26. Close the form and return to your programming environment