I am asked N>=3 sets of dice are thrown. How many way can exactly 3 sixes turn up.

I did the following

for a single set of dice....

dice1+dice2=6 how many solutions?

(5 choose 1)/2ceiling function??? which is 3 ways

so for 3 dice to roll 6 there are...

3x3x3

then the other n-3 dice can roll anything but a six.

so there are 18 unique ways to roll a set of dice

18-3=15 -the total ways to roll a dice with no 6.

so I get...

(3)(3)(3)(n-3)(15) ways.

Now my big problem is how do I express this answer in terms of binomial co-efficient?