What event does the probability ${{n\choose k}\over 6^n}$ describe?

Question

The event "getting $k$ times the number $6$ in $n$ dice throws" has probability ${n\choose k}\cdot({1\over 6})^k\cdot({5\over6})^{n-k}$

So what event corresponds to ${{n\choose k}\over 6^n}$ ?

Answer 1

Just take two random number from $1$ to $6$, say $1$,$2$.

Throwing a dice $n$ times.

Then the probability to have $k$ $1$ appearing and all remaining are $2$ is $ \frac{{n}\choose{k}}{6^n}$.

Which is an extremely low probabilistic event, since the asymptotic estimate of ${n}\choose{k}$ is at most $2^n$.