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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.)

 Jun 3, 2024
 #1
avatar+129487 
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Factor 2000  =  2^4 * 5^3 =  1* 4^2 * 5^3 =   1 * 4 * 4 * 5 * 5 * 5

 

Possible identifiable sequences  =    7!  / [ 2! * 3! ]  =    420

 

cool cool cool

 Jun 3, 2024

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