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.)

tomtom Aug 18, 2024

#1**0 **

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.

lonelychungus Aug 18, 2024

#2**+1 **

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! :)

NotThatSmart Aug 19, 2024