JSFiddle - React, Tailwind, and code Playground

HTML

<div class="select-wrapper">
    <select>
        <option>EEE</option>
        <option>ECE</option>
        <option>EIE</option>
    </select>
</div>

CSS

.select-wrapper {
    display:inline-block;
    border:1px solid #bbbbbb;
    position:relative;
    width:120px;
    -webkit-border-radius:5px;
    -moz-border-radius:5px;
    border-radius:5px;
    margin-top: 10px;
}
.select-wrapper:before{
    content: "";
    position:absolute;
    right: 5px;
    top:8px;
    border-width: 5px 5px 5px 5px;
    border-style: solid;
    border-color: #666666 transparent  transparent  transparent ;
    z-index:3;
}
.select-wrapper:after {
    content:"";
    display:block;
    position:absolute;
    top:0px;
    bottom:0px;
    width:20px;
    right:0px;
    border-left:1px solid #bababa;
    background-color:#ededed;
    -webkit-border-top-right-radius:5px;
    -moz-border-top-right-radius:5px;
    border-top-right-radius:5px;
    -webkit-border-bottom-right-radius:5px;
    -moz-border-bottom-right-radius:5px;
    border-bottom-right-radius:5px;
}
select {
    width:100%;
    background-color:#ededed;
    border:none;
    outline:none;
    padding:0px;
    margin:0px;
    position:relative;
}