+625 Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $2000,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)
+1804 I can only think of two possible combinations to satisfy the conditions given.
We have Combinations of 2, 2, 4, 5, 5, 5 and combinations of 1, 4, 4, 5, 5, 5
There might be others, but I can't think of any other ones.
The number of permutations of 2, 2, 4, 5, 5, 5 is \(6! = 720 \)
The number of permutations of 1, 4, 4, 5, 5, 5 is \(6! = 720 \)
So the total number of sequences would be \(720 + 720 = 1440 \)sequences
So 1440 is the answer.
Thanks! :)
