Suppose I roll a fair dice for 7 times. What is the probability that I will roll all the 6 sides of the dice?

What I have done is this:

$\displaystyle \left ( \frac{1}{6} \right )^6\times 7! = \frac{35}{324}$

But is this correct?

I am not sure if the above is correct because I thought it could be a Negative Binomial distribution too. The 7 throws with 6 sides show up is somewhat daunting and makes the question confusing.