Sum of all arrangement

There are 24 numbers with 1, 2, 3, and 4 as digits. For each of the four digits, say the units digit $d_0$ , 1, 2, 3, and 4 appear the number of times. Therefore, 1 appears 6 times, 2 appears 6 times, 3 appears 6 times and 4 appears 6 times. The sum of units digits is $6 \times \dfrac {4(4+1)}2 = 60$ .

It is the same for the tens (d_1), hundreds $d_2$ , and thousands $d_3$ units. Therefore the sum of all 24 of these numbers is $60 (1+10+100+1000) = 60(1111) = \boxed{66660}$ .

<?php
$arr = range(1,4);
do{
$newarr = array();
foreach($arr as $a){
for($i=1;$i<=4;$i++){
if(!preg_match('@'.$i.'@',$a)){
$newarr[] = $a.$i;
}
}
}
$arr = $newarr;
} while(strlen($arr[0])<4);
echo array_sum($arr); //66660
?>