Hi Abdul,
Add the Dropdown binding code in Post Method as well.
WorkshopActivity_Bl objWs = new WorkshopActivity_Bl();
List<Departments> dpl = objWs.Dept.ToList();
IEnumerable<SelectListItem> items = objWs.Dept.Select(c => new SelectListItem { Value = c.DepartmentID.ToString(), Text = c.DepratmentName });
ViewBag.Dept = items;
Once you add these lines in post method the code should work.
ViewData and ViewBag can be used only in the Single Request. The data will be lost in the PostBack. So you need to set it again.
Also Change the View Code.
You cannot write Model.Dept.DepatmentID to the Model Property Name.
Like Model.Dept.FKDeptID.
This Should help.