Catherine rolls a standard 6-sided die six times. If the product of her rolls is 2500, then how many different sequences of rolls could there have been? (The order of the rolls matters.)
Observe that $2500=2^2\cdot 5^4$. Let \[
2500=\underbrace{5\cdot 5\cdot 5\cdot 5}_{4}\cdot \underbrace{2\cdot 2}_{2}.
\] To form the product $2500$, Catherine must roll four 5's and two 2's. The four 5's can appear on any of the six rolls. The two 2's can also appear on any of the six rolls, except that they cannot appear on the same roll as any of the 5's. Thus there are $6\cdot 5=30$ possible ways to form the sequence of rolls, so our final answer is $\boxed{30}$.