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}