ASPX UpdatePanel - dynamic control events

Question

My scenario: When adding dynamic controls to an UpdatePanel, their events are working properly.

But I want to add a new control to the UpdatePanel from another event (e.g. when a button is clicked).

To implement that, I need to add this control on the button event - but then the new control event do not work. On the other hand, I cannot do it on PageLoad - since it is called before the button event.

Therefore, the function RemoveProfession_Click isn't called on a LinkButton click

  int number_of_buttons=3;
 protected void Button1_Click(object sender, EventArgs e)

    {
        //here the value of number_of_buttons is changed
        Update();
    }

    private void Update()
    {
        LinkButton[] lbRemove = new LinkButton[number_of_buttons];

        for (int i = 0; i < number_of_buttons; i++)
        {
            Label lblProfession = new Label();
            lblProfession.Text = "Label" + i;
            PlaceHolder1.Controls.Add(lblProfession);
            PlaceHolder1.Controls.Add(new LiteralControl("&nbsp;"));

            lbRemove[i] = new LinkButton();
            lbRemove[i].Text = "remove";
            lbRemove[i].CommandArgument = "" + i;
            lbRemove[i].Click += new EventHandler(RemoveProfession_Click);
            lbRemove[i].CausesValidation = false;
            lbRemove[i].ID = "RemoveProfession" + i;
            ScriptManager1.RegisterAsyncPostBackControl(lbRemove[i]);
            PlaceHolder1.Controls.Add(lbRemove[i]);

            PlaceHolder1.Controls.Add(new LiteralControl("<br/>"));
        }
    }

<asp:ScriptManager ID="ScriptManager1" runat="server"></asp:ScriptManager>
    <asp:UpdatePanel runat="server" ID="UpadtePanel1">
        <Triggers>
            <asp:AsyncPostBackTrigger ControlID="Button1" EventName="Click" />
        </Triggers>
        <ContentTemplate>
            <asp:PlaceHolder runat="server" ID="PlaceHolder1">
                <asp:Label runat="server" ID="Label1" Text="Text1"></asp:Label>
            </asp:PlaceHolder>
        </ContentTemplate>
    </asp:UpdatePanel>
    <asp:Button runat="server" ID="Button1" OnClick="Button1_Click" />