Edit in JSFiddle

<button id="button">rkbr</button>


<select id="select">
    <option>eee</option>
    <option>eee</option>
    <option>eee</option>
    <option>eee</option>
    <option>eee</option>
    <option>eee</option>
    <option>eee</option>
    <option>eee</option>
</select>

              
$("#button").on("click",function(){
        $("#select").trigger("click");
 });