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Catherine rolls a 6-sided die five times, and the product of her rolls is 300. How many different sequences of rolls could there have been? (The order of the rolls matters.)

 Apr 13, 2022
 #1
avatar+1384 
+1

The prime factorization of 300 is \(2 \times 2 \times 3 \times 5 \times 5\)

 

There are \({5! \over 2! 2!} = \color{brown}\boxed{30}\) ways to order these. 

 Apr 13, 2022
 #2
avatar+122 
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It 30 

 Apr 13, 2022
 #3
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12556, 13455, 22355==3 combinations.


12556 ==5! / 2! ==60 permutations
13455 ==5! / 2! ==60 permutations
22355 ==5! / 2!2!==30 permutations


60  +  60  +  30 ==150 permutations - or such sequences.

 Apr 13, 2022
 #4
avatar+326 
+1

Dang, there are a lot of CPhills here!!!

 Apr 13, 2022

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