Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $480,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)
480 = 2^5 * 3 * 5 =
2 * 4 * 4 * 3 * 5 * 1 = 6! / ( 2!) = 360
6 * 4 * 4 * 5 * 1 * 1 = 6! / ( 2! * 2!) = 180
360 + 180 =
540 possible sequences
+1237 
