Take a look at the following link: http://jsfiddle.net/sarfarazdesigner/K2ndZ/5/ where you need to make some changes to the CSS.
.combobox {cursor:pointer;display:inline-block; position:relative;}
.combobox .selector {position:relative; float:left; }
.combobox .selector p{border:1px solid #cccccc;padding: 2px 5px;}
.combobox ul {padding:0;margin:0;display:inline-block;border:1px solid #eeeeee;background-color:#cccccc;}
.combobox li {padding: 2px 5px}
This is the HTML code:
<div class="combobox">
<div class="selector">
<p>Please select</p>
<ul>
<li>Option 1</li>
<li>Option 2</li>
<li>Option 3</li>
</ul>
</div>
<div class="selector">
<p>Please select</p>
<ul>
<li>Option 1</li>
<li>Option 2</li>
<li>Option 3</li>
</ul>
</div>
</div>
This is the jQuery part:
$(document).ready(function(){
$('.combobox ul').hide();
$('.combobox p').hover(
function(){
console.log(this);
$(this).next('ul').stop().slideDown();
},
function(){
$(this).next('ul').stop().slideUp();
}
);
$('.combobox li').click(function(){
$(this).parents('.combobox').find('.selector').text($(this).text());
});
});
Here is the updated link based on your requirements:
http://jsfiddle.net/sarfarazdesigner/K2ndZ/7/