If P represents the product of the first 13 positive integers, which

Tough and Tricky questions: Number Properties.

If P represents the product of the first 13 positive integers, which of the following must be true?

I. P is an odd number
II. P is a multiple of 17
III. P is a multiple of 24

A) I only
B) II only
C) III only
D) None of the above
E) All of the above

Kudos for a correct solution.

Source: Chili Hot GMAT