<?php

$timeOfDay = $_POST["session"] //change session to the name in the ID feild for the checkbox/radio button.

$db =& JFactory::getDBO();

// Change appointments to the name of the table used for storing the appointments
// Change session to the name of the row in the table for the session EG: am/pm
$query = "
    SELECT COUNT(*)
        FROM appointments
    WHERE session=`".$timeOfDay."`;
";
$db->setQuery($query);
$count = $db->loadResult();
if ( $count > 70 ) { //Change 70 to the threshold for ammout of appointments.
  echo 'Sorry, all the passes have gone.';
  return;
}