(PHP) Probability of two random strings be same - random

Question

I have this code for generating random strings
public function random_string($length = 5)
{
$chars = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz1234567890';
return substr(str_shuffle($chars),0,$length);
}
So, is it possible that two generated strings can be same ?
In my case, there can be a maximum of 62P5 (using permutation) numbers of strings of 5 characters.
But whats the possibility that the 10th & 1000th generated random strings be same ?

Answer 1

This is known as the birthday problem and can be solved by
$chars = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz1234567890';
$length = 5;
$numChars = strlen($chars);
$numberOfStringsGenerated = 50000;
print "numStringsGenerated: " . $numberOfStringsGenerated . "\n";
print "numChars: " . $numChars . "\n";
print "lengthOfString: " . $length . "\n";
$totalPerms = 1;
for ($ii=0; $ii<$length; $ii++) {
$totalPerms *= $numChars - $ii;
}
print "totalPerms: " . $totalPerms . "\n";
$totalProbablity = 1;
for ($ii=0; $ii< $numberOfStringsGenerated; $ii++) {
$totalProbablity *= ($totalPerms - $ii)/$totalPerms;
}
print "Probablity: ";
print 1 - $totalProbablity . "\n";
Here is the codepad output
Here is the Wikipedia page
This calculation assumes that the PRNG for the str_shuffle is good enough for all permutations to be equally likely, which won't be exactly true, especially as the number of chars increases.

Answer 2

Obviously that is possible.
The right way to do this, is store already used strings in a database.
I use this in a system that generates a random session token that is stored at database.
Always that I generate a new random session token, i query for it in session table. If no results, OK, else, generate a new token.
The probability is very low, but not impossible, and everytime you insert new tokens at table, the probability of overwriting just grow.