Here's my redesign. You're reassigning (50*49), (49*48), (48*47)... to $probability every time through the loop.

#!/usr/bin/perl -w

use strict;
# use integer;

my $probability = permutation(50,5);
 
print ($probability * 36);

sub permutation {
    my $probability = 1;
    my ($number, $times) = @_;

    print "The times is $times and the number is $number.\n";

    while ($times-- > 0) {
        $probability *= $number;
        $number--;
    }
    return $probability;
}
[download]

Commenting out 'use integer' does slow it down. In its defense, it does avoid a type overflow which gave me an incorrect result of 563108608.

For what it's worth, I have a different type of lottery script generating data at my homepage. I can post it, as it might be interesting.