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This isn't tested, so take it with a grain of salt, but I think it should work : EDIT : Code revised.

class Mage_Catalog_Block_Product_List_Random extends Mage_Catalog_Block_Product_List
{
    protected function _getProductCollection()
    {
        if (is_null($this->_productCollection)) {
            $categoryID = $this->getCategoryId();
            if($categoryID)
            {
                // Get array of subcategory ids
                $catModel = Mage::getModel('catalog/category');
                $parentCat = $catModel->load($categoryID);
                $children= explode(',',$parentCat->getChildren());
                

                // Use the array to filter the collection
                $collection = Mage::getModel('catalog/product')->getCollection();

                $collection->joinField(
                    'category_id', 'catalog/category_product', 'category_id',
                    'product_id = entity_id', null, 'left'
                )
                    ->addAttributeToFilter('category_id', array('in' => $children))
                    ->addAttributeToSelect('*');
            $collection->getSelect()->group('entity_id');
            } else {
                $collection = Mage::getResourceModel('catalog/product_collection');
            }
            Mage::getModel('catalog/layer')->prepareProductCollection($collection);
            $collection->getSelect()->order('rand()');
            $collection->addStoreFilter();
            $numProducts = $this->getNumProducts() ? $this->getNumProducts() : 3;
            $collection->setPage(1, $numProducts)->load();

            $this->_productCollection = $collection;
        }
        return $this->_productCollection;
    }
}