Catherine rolls a 6-sided die six 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.)
124556 ( 360 ) , 222556 ( 60 ) , 223455 ( 180 ) , 344556 ( 180 ) , >>Total combinations = 4
>>Totals in parentheses = 780 permutations
+118608 I do not want to do it all for you.
Start by finding the prime factors of 1200.
You should know immediately from that what 2 of the rolls will have to be.
There are only 4 possibililites for what the rest will be.
then you just have to work out how many ways each of those 4 sets of 6 numbers can be ordered.
Give it a go. :)
