All right, I figured it out. But if someone wants to suggest something better, please feel free and I will mark it correct.
// array of previously-assigned numbers (get this by looping through the registered users -not shown)
$numbers_already_taken = array(3,8,1);
// get all the numbers between 1-10
$numbers = range(1, 10);
// shuffle the numbers so they are in random order
shuffle($numbers);
// set up variable to hold this user's draw #
$draw = '';
// loop through the available numbers
foreach ($numbers as $number) {
// ignore numbers that have already been assigned
if (!in_array($number, $numbers_already_taken)) {
// assign the first matching draw number (break stops it)
$draw = $number;
break;
}
}
echo 'Your Draw Number: ' . $draw;
// save $draw to the user's profile or booking (not shown)