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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.)

 Aug 8, 2024
 #1
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I can only think of two possible combinations to satisfy the conditions given.

We have Combinations of 2, 2, 4, 5, 5, 5 and combinations of 1, 4, 4, 5, 5, 5    

There might be others, but I can't think of any other ones. 

 

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   

 

So 1440 is the answer. 

 

Thanks! :)

 Aug 8, 2024
edited by NotThatSmart  Aug 8, 2024

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