Dropdownlist ASP.NET MVC not updating Model

I have two Model classes like so:

Program:

public class Program
{
    public int ProgramId { get; set; }

    public string Name { get; set; }

    public virtual Playlist chosenPlaylist { get; set; }

    public virtual IList<Playlist> Playlists { get; set; }
}

public class Playlist
{
    public int PlaylistId { get; set; }

    public string Name { get; set; }

    public int NumberVotes { get; set; }

    public virtual IList<Song> Songs { get; set; }
}

In my Edit Program View, I want to update the chosenPlaylist so I can allow the user to select none or one of the Program's Playlists.

For example:

Program 1:

• Playlist 1
• Playlist 2

Chosen Playlist: Playlist 1

So the user can then edit and select None (so no playlist), 1 (won't change anything) or 2 and that gets saved to the database.

I've tried to create a dropdownlist in my Controller but it won't update.

Here's what I have in both my GET and POST Edit ActionResults:

ViewBag.chosenId = new SelectList(program.Playlists, "PlaylistId",
"Name", program.chosenPlaylist.PlaylistId);

And in my View:

@Html.DropDownList("PlaylistId", (SelectList)ViewBag.chosenId)

This displays the list fine and pre-selects the chosen Playlist, if there is one (if not, I'll write code for it to default to the first). If there aren't playlists in a Program, that's easy to control.

However, problems:

• Doesn't update my model. If Playlist 2 is the chosen one, for example, and I choose P1, it continues to display P2 after the POST event.
• I want to include an option in the dropdownlist for it not to pick any value (so, place a NULL in that field). Is that possible?

There are no errors thrown, everything seems to work except for the most important part - updating the database.