Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $100,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)
Here's what I find
100 = 10 * 10 * 1 * 1 =
2 * 5 * 2 * 5 * 1 * 1 identifiable sequences = 6! / ( 2! * 2! * 2!) = 90
4 * 5 * 5 * 1 * 1 * 1 identifiable sequences = 6! / (3! * 2!) = 60
Total identifiable sequences = 150
+1557 
