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Catherine rolls a standard 6-sided die five times, and the product of her rolls is 900 How many different sequences of rolls could there have been? (The order of the rolls matters.)

 Apr 3, 2023
 #1
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To find how many different sequences of rolls could there have been given that Catherine rolls a standard 6-sided die 5 times and the product of her rolls is 900 (the order of the rolls matters), we can use the following approach:

One way to find the sequences is to factorize the number 900 into its prime factors 12. Since 900 = 2^2 * 3^2 * 5^2, we need to find all the possible combinations of five numbers chosen from the set {2, 2, 3, 3, 5, 5}. We can use the formula for combinations with repetition and consider each number as a distinct item. The number of sequences is then given by:

(5 + 6 - 1)! / (5! * (6 - 1)!) = 126

 Apr 3, 2023
 #3
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Thank you!

Guest Apr 5, 2023
 #2
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15566==5!/2!2!  ==30 permutations 

23556==5!/2!     ==60 permutations

33455==5!/2!2!  ==30 permutations

 

Total ==30 + 60 + 30 ==120 - number of possible sequences of rolls.

 Apr 3, 2023
 #4
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The correct answer is 126, but thanks for trying!

Guest Apr 5, 2023

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