AMC 12 2001 Problem 5

What is the product of all positive odd integers less than 10000?

$\text{(A)}\ \dfrac{10000!}{(5000!)^2} \text{(B)}\ \dfrac{10000!}{2^{5000}} \text{(C)}\ \dfrac{9999!}{2^{5000}} \text{(D)}\ \dfrac{10000!}{2^{5000} \cdot 5000!} \text{(E)}\ \dfrac{5000!}{2^{5000}}$