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Catherine rolls a standard $6$-sided die six times.  If the product of her rolls is $100,$ then how many different sequences of rolls could there have been?  (The order of the rolls matters.)

 Jan 11, 2024
 #1
avatar+128448 
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Here's what I find

 

100 =  10 * 10 *  1 * 1  = 

 

2 * 5 * 2 * 5 * 1 * 1     identifiable sequences  =  6!  / ( 2! * 2! * 2!)  = 90

 

4 * 5 * 5 * 1 * 1  * 1   identifiable sequences =   6! / (3! * 2!)  = 60

 

Total identifiable sequences  = 150

 

cool cool cool

 Jan 11, 2024

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