1. C Hint: Consider the generating function $f(t)=\left(1+t+t^{2}+t^{3}\right)\left(1+t^{2}+\left(t^{2}\right)^{2}+\left(t^{2}\right)^{3}\right)\left(1+t^{5}\right)=\cdots+8 t^{9}+\cdots$, the coefficient of $t^{9}$ is 8.
1. Now there are 3 1-gram weights, 3 2-gram weights, and 1 5-gram weight. For a 9-gram object, how many different ways can it be weighed (weights are only allowed on one side of the balance)?
A. 6
B. 7
C. 8
D. 9