Step-by-Step Solution
Key Concept: Find prime factorization of $10!$. Sum of odd divisors = product of sums over odd primes only.
Sum of odd divisors $=\frac{3^5-1}{2}\cdot\frac{5^3-1}{4}\cdot\frac{7^2-1}{6}=121\times31\times8=30008$.
Correct Answer: (C) 30008