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Catherine rolls a 6-sided die five times, and the product of her rolls is 1500. How many different sequences of rolls could there have been? (The order of the rolls matters.)

 Feb 1, 2021
 #1
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25556 , 25565 , 25655 , 26555 , 34555 , 35455 , 35545 , 35554 , 43555 , 45355 , 45535 , 45553 , 52556 , 52565 , 52655 , 53455 , 53545 , 53554 , 54355 , 54535 , 54553 , 55256 , 55265 , 55345 , 55354 , 55435 , 55453 , 55526 , 55534 , 55543 , 55562 , 55625 , 55652 , 56255 , 56525 , 56552 , 62555 , 65255 , 65525 , 65552 , Total =  40 such rolls

 Feb 1, 2021
 #2
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+1

1500  =

 

3 * 5  *  5^2  *  2^2  = 

 

3 *  5^3  * 2^2

 

Possible combos

35554   =  5! / 3!   =     20  identifiable sequences

55562  =   5!  /3!  =      20  identifiable squences

 

So....just as  the guest found......40  identifiable sequences  !!!

 

cool cool cool

 Feb 1, 2021

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