How can I send multiple value for a form element when posting data through ajax ?

How can I send multiple value for a form element when posting data through ajax ?

I am creating a search form using ajax, I've a field for Bedrooms and I've used radio buttons as Double, Single and Both. The only problems lies with selection 'Both' which gives no positive result. The 'Both' actually is not a value but I want to fetch Bedrooms of both Double and Single Type.
I wrote following code on change event of radio button.
  1.   var $form = $("#frm1");
                          url = $form.attr( 'action' );
                         formdata = $form.serialize();
                         formdata = $form.serializeArray();
                         formdata = $.grep(formdata,function(o,i){ return o.value != 'Both'; });
                         formdata = formdata + "&CAT_Custom_228468=Double&CAT_Custom_228468=Single";
                         formdata = $.param(formdata);
               $.post( url, $.param(formdata),
                        function( data ) {
                                $( "#results").html("");
                                $("#loader").hide();
                                $( "#results" ).empty().append( $(data).find("#results").html());
    });
Can you guys tell me how can I fetch Bedrooms for both type ?