+0  
 
0
4
2
avatar+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.)

 Aug 18, 2024
 #1
avatar+8 
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. 

 Aug 18, 2024
 #2
avatar+1858 
+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! :)   

 Aug 19, 2024
edited by NotThatSmart  Aug 19, 2024

2 Online Users

avatar