statistics - How do you calculate probability of rolling all faces of a die after n number of rolls?

Im pretty new to the stackexchange, and posted this is statistics, and then discovered this site, and thought it was much more appropriate, so here I go again:

It is fairly easy to figure out what is the average rolls it would take to roll all faces of a die [1 + 6/5 + 6/4 + 6/3 + 6/2 + 6/1 = 14.7], but that got me thinking of a seemingly more complicated problem.

Say you roll a die 1-5 times, the is the odds of ALL faces showing, is obviously 0. If you roll a die 6 times, the odds of all faces showing can easily be calculated like so:

1 * (5/6) * (4/6) * (3/6) * (2/6) * (1/6) = .0154 or 1.54%

Now is where I get stuck. How to do 7, or more times, and calculate it with n.

Any tips is helpful!