2. For the above problem, if the weights are allowed to be placed on both ends of the balance, and it is assumed that the weights are all different (i.e., even identical weights must be numbered), then the number of different ways to weigh a 10-gram object is
A. 28
B. 29
C. 30
D. 31
2. B Consider the generating function $f(t)=\left(t^{-1}+1+t\right)^{3}\left(t^{-2}+1+t^{2}\right)^{3}\left(t^{-5}+1+t^{5}\right)$, expand it, and the coefficient of $t^{10}$ can be found to be 29.