+1926 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.)
+8 1. Figure out combinations that multiply to 2000.
2. Then, figure out the number of permutations in each sequence.
3. Add the number of permutations together.
+1946 I can only think of two combinations I can think of are
Combinations of 2,2,4,5,5,5 and combinations of 1,4,4,5,5,5
Now, we can calculate the number of ways or organize each combination and add them together.
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
Now, we had these together to get
720+720=1440.
So I think this is the correct answer, but I'm not actually very sure.
Thanks! :)
