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.)

bader Dec 25, 2023

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*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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Bosco Dec 25, 2023