Magento random item on homepage

i am new at Magento, and i encountered my first problem. That items will show randomly on homepage.

I have this code:

<?php 

$_productCollection->getSelect()->order(new Zend_Db_Expr('RAND()'));
$_items = $_productCollection->getItems(); 
?>

<?php if ($_collectionSize && $tmpHtml = $this->getChildHtml('block_category_above_collection')): ?>
    <div class="block_category_above_collection std"><?php echo $tmpHtml; ?></div>
<?php endif; ?>

<?php if(!$_collectionSize): ?>
    <?php if ($tmpHtml = $this->getChildHtml('block_category_above_empty_collection')): ?>
        <div class="block_category_above_empty_collection std"><?php echo $tmpHtml; ?></div>
    <?php else: ?>

And when is change it to

<?php
$_productCollection=$this->getLoadedProductCollection();
$_collectionSize = $_productCollection->count();
shuffle($_productCollection);

?>

it's showing me fatal error.

I even tried this

    <?php
// $_productCollection = $this->getLoadedProductCollection();
 $_helper = $this->helper('catalog/output');
 $_category = Mage::getModel('catalog/category')->load($this->getCategoryId());
 $_productCollection = Mage::getResourceModel('reports/product_collection')
                       ->addAttributeToSelect('*')
                       ->addCategoryFilter($_category)
                       ->setVisibility(array(2,3,4));
 $_productCollection->getSelect()->order(new Zend_Db_Expr('RAND()'));                  
 $_productCollection->setPage(1, 4);

?>

But nothing helped. What am i doing wrong ?