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Catherine rolls a standard 6-sided die six times, and the product of her rolls is \(2500\).  How many different sequences of rolls could there have been?  (The order of the rolls matters.)

 May 13, 2023
 #1
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Catherine rolls a standard 6-sided die six times. If the product of her rolls is \(2500\), then how many different sequences of rolls could there have been? (The order of the rolls matters.)

 May 13, 2023
 #2
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There are 2 combinations as follows:

 

145555 ==6!/4! ==30 permutations

225555==6!/4!2!==15 permutations

 

Total == 30  +  15 ==45 different sequences of rolls. 

 May 13, 2023

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