There are 5 places to put the o. Then there are 4 places left to put the r. Then there are 3 places left to put the i. The remaining 2 places are filled with n.

5 x 4 x 3 = 60

There's a recipe [1] in the online Python Cookbook to calculate permutations and combinations of elements in a list, using Python's generators. You'll need to remove duplicates from the results, since the two n's are perceived as different tokens; but you'll eventually end up with 60 possibilities.

[1] http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/190465

Sjoerd: All mathmatical formulas must be proven with long, inefficient, brute force Perl algorithms. -grin-

See http://www.oreillynet.com/pub/wlg/5492 for brian d foy's generic solution.

No need to reinvent the wheel:

use Algorithm::FastPermute ('permute');
my @letters = qw/o r n i n/;
my %seen;
permute {
my $word = join "", "m", @letters, "g";
print "$word\n" unless $seen{$word}++;
} @letters;