Catherine rolls a 6-sided die five times, and the product of her rolls is 1200. How many different sequences of rolls could there have been? (The order of the rolls matters.) I'm having trouble with the casework on this one. I know the factorization of 1200 is 2^4*3*5^2 but I don't know how to arrange my casework to account for the fact that 6 could be a possibility. PLEASE don't put the answer, I just want a push in the right direction. Could someone help? Thanks!
You have rolled a die 5 times, which is the same as rolling 5 dice once. Each die is numbered from 1 to 6. What combinations of the 6 numbers will give you a product of 1200?
Well, the only ones that work are: 2 x 4 x 5 x 5 x 6 and 3 x 4 x 4 x 5 x 5. Now, how many DISTINCT permutations can you get out of the 5 numbers, bearing in mind that you have 2 fives and 2 fours?