Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $2000,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)
Factor 2000 as 2^4 * 5^3 = 2 * 2 * 2^2 * 5 * 5 * 5 = 2 * 2 * 4 * 5 * 5 * 5
The number of identifiable sequences is
6! 720
_______ = _____ = 60
2! * 3! 12
+1459 
