The vertices V of a centrally symmetric hexagon in the complex plane are given by
V=\left\{\sqrt{2} i,-\sqrt{2} i, \dfrac{1}{\sqrt{8}}(1+i), \dfrac{1}{\sqrt{8}}(-1+i), \dfrac{1}{\sqrt{8}}(1-i), \dfrac{1}{\sqrt{8}}(-1-i)\right\} .
For each j, 1 \leq j \leq 12, an element z_{j} is chosen from V at random, independently of the other choices. Let P=\prod_{j=1}^{12} z_{j} be the product of the 12 numbers selected. What is the probability that P=-1 ?
Answer Choices
A. \dfrac{5 \cdot 11}{3^{10}}
B. \dfrac{5^{2} \cdot 11}{2 \cdot 3^{10}}
C. \dfrac{5 \cdot 11}{3^{9}}
D. \dfrac{5 \cdot 7 \cdot 11}{2 \cdot 3^{10}}
E. \dfrac{2^{2} \cdot 5 \cdot 11}{3^{10}}