Number of combinations of 30 dice rolls

[njl86]

You roll thirty dice.
How many different possible combinations can be rolled?
Order does not matter

I think it's 6^30 choose 30, so:
$$\frac{(6^{30})!}{(6^{30}-30)!(30!)}$$

Also, perhaps the more important part of my question - any idea how to approximate this? The numbers involved are very large

 

[awkward]

If you are simply counting the number of 1s, 2s, 3s, ..., 6s, the number of possibilities is
$$\binom{35}{30} = \frac{35!}{30! \; 5!}$$

See http://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)