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 = 2^4 * 5^3 = 1* 4^2 * 5^3 = 1 * 4 * 4 * 5 * 5 * 5
Possible identifiable sequences = 7! / [ 2! * 3! ] = 420
+1839 
