Three distinct integers are selected at random between 1 and 2016, inclusive. Which of the following is a correct statement about the probability p that the product of the three integers is odd?
Answer Choices
A. p<\dfrac{1}{8}
B. p=\dfrac{1}{8}
C. \dfrac{1}{8}<p<\dfrac{1}{3}
D. p=\dfrac{1}{3}
E. p>\dfrac{1}{3}