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Catherine rolls a standard 6-sided die six times. If the product of her rolls is \(2500 \) then how many different sequences of rolls could there have been? (The order of the rolls matters.)

 

 

\(\phantom{If the product of her rolls is  2700}\)

 Jun 26, 2023
 #1
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The rolls must be 1, 2, 5, 5, 6 in some order, so there are 5!/2 = 60 ways.

 

There are more ways though. For example, there could be:

 

1, 3, 4, 5, 5

2, 2, 3, 5, 5

 

This gives another 90 ways:

 

1, 3, 4, 5, 5: 5!/2 = 60

2, 3, 3, 5, 5: 5!/4 = 30

 

If you add it with the previous one, we get 60+60+30 = 150

 Jun 27, 2023
 #2
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There are only 2 combinations as follows:

 

2500=2^2 x 5^4

 

145555 = 6! / 4! =30

225555 = 6! / 4!2!=15

 

Total = 30 + 15 = 45 different sequences of rolls

 Jun 27, 2023

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