+1911 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.
+1908 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! :)
