+1768 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.)
+1277
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.)
Combinations of 2, 2, 4, 5, 5, 5 and combinations of 1, 4, 4, 5, 5, 5
I cannot think of any other combinations that would multiply to 2000.
The number of permutations of 2, 2, 4, 5, 5, 5 is 6! = 720
The number of permutations of 1, 4, 4, 5, 5, 5 is 6! = 720
So the total number of sequences would be 720 + 720 = 1440 sequences
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