One more thing you may wish to consider is using algorithms that do not rely on large integers. For example, instead of computing ncr( $n, $r ) ("n choose r") by the formula $n! / ($n! * ($n-$r)!), use the following approach:

sub ncr {
    my( $n, $r ) = @_;
    my( $i, $result );
                                                                      
+                                                                     
+                
    $result = 1;
    for $i ( 1 .. $r ) {
        $result *= $n - $r + $i;
        $result /= $i;
    }
    return $result;
}
                                                                      
+                                                                     
+                
print "ncr( 6, 3 ) = ", ncr( 6, 3), "\n";
# ncr( 6, 3 ) = 20
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That is, arrange your multiplications and divisions in such a way that at any given point of time you have an integer not much larger than the output.