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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.)

 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   

.

 Dec 25, 2023

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