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Catherine rolls a standard $6$-sided die six times.  If the product of her rolls is $480,$ then how many different sequences of rolls could there have been?  (The order of the rolls matters.)

 Jun 22, 2024
 #1
avatar+129725 
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480 = 2^5 * 3  * 5  = 

 

2 * 4 * 4 * 3 * 5 * 1 =    6! / ( 2!) =   360

 

6 * 4 * 4 * 5 * 1 * 1 =  6! / ( 2! * 2!)  =  180

 

360 + 180  =  

 

540 possible sequences

 

cool cool cool

 Jun 22, 2024

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