With radio buttons they cannot select ALL of them if the "name" is the same.
They can do that with checkboxes, but not radio buttons.
See this test script.
You have already given each radio button a value in your form.
Now you just need to see which one they picked ...
PHP Code:
<?php
$option="none";
if($_POST['delivery'])){
$option=$_POST['delivery'];
)
echo "The radio button they selected was: ".$option;
?>
EDIT: fixed typo
.