11. When seven standard dice are thrown, the probability that the sum of the numbers on the top faces is 10 is $\frac{n}{6^{7}}\left(n \in \mathbf{Z}_{+}\right)$. Then the value of $n$ is ( ).
(A) 42
(B) 49
(C) 56
(D) 63
(E) 84
11. E.

The required is the number of solutions to the equation
$$
x_{1}+x_{2}+\cdots+x_{7}=10\left(x_{i} \in \mathbf{Z}, 1 \leqslant x \leqslant 6\right)
$$

Using the stars and bars method: Place three dividers into the spaces between 10 ones, there are $\mathrm{C}_{9}^{3}=84$ ways.