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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 16, 2023
 #1
avatar+126978 
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Factor  2000  as    2^4 * 5^3 =  2 * 2 * 2^2 * 5 * 5 * 5 =  2 * 2 * 4 * 5 * 5 * 5

 

The number of identifiable sequences is

        

                6!                         720

          _______  =              _____  =     60

           2! *  3!                       12

 

cool cool cool

 Dec 16, 2023

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