+721 Catherine rolls a standard 6-sided die eight times. If the product of her rolls is 2700, then how many different sequences of rolls could there have been? (The order of the rolls matters.)
+129771 prime factorization of 2700 = 2^2 * 3^3 * 5^2
Possible Factorizations Number of identifiable sequences
22333551 8! / (2! * 3! * 2!) = 3360
43335511 8! /( 2! * 3! * 2! ) = 3360
62335511 8! / ( 2! * 2! * 2!) = 5040
66355111 8! / ( 2! * 2! * 3!) = 3360
Total possible sequences = 3 (3360) + 5040 = 15120
