$11 \cdot 8$ Expand $\left(1-\frac{1}{a}\right)^{6}$, the sum of the coefficients of its last three terms is
(A) 22.
(B) 11.
(C) 10.
(D) -10.
(E) -11.
(13th American High School Mathematics Examination, 1962)
[Solution] Using Pascal's Triangle, we know the coefficients of the expansion of $(a+b)^{n}$ are sequentially
$$
\begin{array}{l}
1 \\
11 \\
\begin{array}{lll}
1 & 2 & 1
\end{array} \\
\begin{array}{llll}
1 & 3 & 3 & 1
\end{array} \\
\begin{array}{lllll}
1 & 4 & 6 & 4 & 1
\end{array} \\
\begin{array}{llllll}
1 & 5 & 10 & 10 & 5 & 1
\end{array} \\
\begin{array}{lllllll}
1 & 6 & 15 & 20 & 15 & 6 & 1
\end{array} \\
\text {................................... } \\
\end{array}
$$

Given that the coefficient of the second term in the binomial is -1, the coefficients of the last three terms should be $15, -6, 1$. Their sum is
$$
15-6+1=10 \text {. }
$$

Therefore, the answer is $(C)$.