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.)

AnswerscorrectIy Aug 8, 2024

#1**+1 **

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! :)

NotThatSmart Aug 8, 2024