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.)
+1347 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
