Simple, you're doing it backwards. Pick a doctype, and write your code to fit that. Or in your case, alter your code to fit it. Use the W3C Validator to assist you.
I personally like XHTML Transitional, requires you to write code very cleanly but it does wonders for cross-browser consistency.
I think what you want to do here is just have 2 separate forms on the same PHP page. Make sure the text areas have a different id attribute so you can differentiate them. Both forms can submit to the same page, just check the id in the POST to see which one you've got. Hope this helps.
Something like this
<?php
if($_POST[radioelem]==="num3" && $_POST[optionelem]==="num4")
{
echo "You selected 3 and 4";
}
?>
where radioelem and optionelem are the names of your form elements and num3 and num4 are the values assigned to the options.