The symmetric group $S_n$ has $\factorial{n}$ elements, hence it is not true that $S_{10}$ has 10 elements. Find the characteristic of the ring 2Z.

A: Let’s think step by step. A characteristic of a ring is R is $n$ if the statement $ka = 0$ for all $a\in 2Z$ implies that $k$ is a multiple of $n$. Assume that $ka = 0$ for all $a\in 2Z$ for some $k$. In particular $2k = 0$. Hence $k=0$ and $n=0$. The answer is (A).

A: Let’s think step by step. The amount of light is proportional to the aperture area $A = \pi D^2/4$ for a lens with diameter $D$, so the relative amounts of light between the eye with diameter 5mm and the telescope with diameter 50mm is $(50 cm)^2/(5mm)^2 = 10000$. The answer is (E).