I want to show the select options when i click sth. button

i try:

    <button id="showSelect">show</button>
    <select id="mySelect">
        <option value="1">1</option>
        <option value="2">2</option>
        <option value="3">3</option>
    </select>
   <script>
        $(document).ready(function() {
            $('#showSelect').on('click', () => {
                $('#mySelect').focus()
            })
        });
    </script>

???????? It doesn’t work…..
then i try:

    <button id="showSelect">show</button>
    <select id="mySelect">
        <option value="1">1</option>
        <option value="2">2</option>
        <option value="3">3</option>
    </select>
   <script>
        $(document).ready(function() {
            $('#showSelect').on('click', () => {
                $('#mySelect').trigger('click')
            })
        });
    </script>

???????? It doesn’t work too…..damn!!

so, how can i do…..