How to set default value in select dropdown option

I have this code

Controller:

public $leave_applicable_genders = [
    "1" => "Both",
    "2" => "Male",
    "3" => "Female",
]; 

public function create()
{
    $leavetype = new HrLeaveType();
    
    return view('leave.leave_types.create')
            ->with('leavetype', $leavetype)
            ->with('leave_applicable_genders', $this->leave_applicable_genders);
}

view:

     <td width="15%">                    
          <select class="form-control select2bs4" data-placeholder="Select Applicable Gender" tabindex="1" name="leave_applicable_gender[]">
               @foreach($leave_applicable_genders as $k => $leave_applicable_gender)
                   <option value="{{$k}}" @if(old("leave_applicable_gender") == "$k") selected @endif>{{$leave_applicable_gender}}</option>
               @endforeach                                         
           </select>
     </td>     

1. How do I set the default value of the select dropdown option to 1 (Both)?

2. The old() helper is not working. How do I rectify this?

Thanks