Databinding combobox using DataContext Problem

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C#

C#4.0

I have 2 tables student and department, in SQLServer

Departmet: with the Following fields
1. DepartmentID (PrimaryKey, AllowNull=false)
2. DepartmentName (Field, AllowNull=False)

Student: with the Following fields
1. StudentID [PrimaryKey, AllowNull=false]
2. StudentName [Field, AllowNull=False]
3. Department_ID [ForeignKey(Department Table), AllowNull=False]

In VS.Net Projects's addnewItem i added LINQToSQl class, then drag n drop these 2 tables and It created a datacontext.

1. Now i have a datagridview:
-> datasource is set to student table

2. I added 2 columns in the datagridview(AutogenerateColumn= false)

1. Student Name(TextBoxColumn)
-> datapropertyname is the StudentName Field of the Student table

2. Department(Comboboxcolumn)
-> Datasource is the Department table
-> ValueMember : "DepartmentID"( PrimaryKey of the DepartmentTable)
-> DisplayMember : "DepartmentName"(Field in the Department table)
-> Datapropertyname is the Department_ID field of the Student Table

Code:

DataClasses1DataContext dc = new DataClasses1DataContext();
private void Form1_Load(object sender, EventArgs e)
        {
             dc.Log = Console.Out;
 
             BindingSource bsDepartment = new BindingSource();
             bsDepartment.DataSource = dc.GetTable<DepartmentTable>().GetNewBindingList();

             BindingSource bsStudent = new BindingSource();
             bsStudent.DataSource = dc.GetTable<StudentTable>().GetNewBindingList();

             dgvStaffMaster.AutoGenerateColumns = false;
             dgvStaffMaster.DataSource = bsStudent;

             DataGridViewTextBoxColumn colName = new DataGridViewTextBoxColumn();
             colName.Name = "StudentName";
             colName.HeaderText = "Student Name";
             colName.DataPropertyName = "StudentName";
             dgvStaffMaster.Columns.Add(colName);

            DataGridViewComboBoxColumn coldept = new DataGridViewComboBoxColumn();
            coldept.Name = "Department_ID";
            coldept.HeaderText = "Department";
            coldept.DataSource = bsDepartment;
            coldept.ValueMember = "DepartmentID";
            coldept.DisplayMember = "DepartmentName";
            coldept.DataPropertyName = "Department_ID";
            dgvStaffMaster.Columns.Add(coldept);

        }

        private void btnSave_Click(object sender, EventArgs e)
        {
            dc.SubmitChanges();  //I use this to to save the changes
        }

PROBLEM:
Every thing works fine if i Edit the Contents of the datagridview,
but if i try to add a newItem, in the NewRow of the Datagridiview, InvalidComboboxCellValue exception is thrown.
But if i set the AllowNull Property of the Department_ID field of the student table to true, Every thing Works Fine!

3. Department_ID [ForeignKey(Department Table), AllowNull=True]
But i need the it to be false, Please Help!

I'm breaking my head for the past one week!

Please Help Me,