Your question seems similar to this one:
how to limit and display tag?
Based on it you can use this code to limit the tags:
$post_tags = get_the_tags();
shuffle($post_tags); // use this incase you want to pick the tags randomly
$count = 0;
if ($post_tags) {
foreach($post_tags as $tag) {
$count++;
echo '<a href="'.get_tag_link($tag->term_id).'">'.$tag->name.'</a> ';
if( $count > 4 ) break;
}
}
It will return 3 tags only.