Catherine rolls a $6$-sided die five times, and the product of her rolls is $300.$ How many different sequences of rolls could there have been? (The order of the rolls matters.)
Here's what I get
1 2 5 5 6 identifiable sequencwa = 5 ! / 2 ! = 60
2 2 3 5 5 identifiable sequences = 5 ! / (2! * 2!) = 30
1 3 4 5 5 identifiable sequences = 5 ! / 2 ! = 60
= 150 sequences
