+241 Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $6,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)
+118680 You could have 5 ones and a 6. The six can be any of the tosses so that is 6 ways (for 6 tosses.)
Or you could roll a 2, a 3 and four 1's in any order.
you have 1 1 1 1 there are 5 places where you can slot in a 2
Now you have X X X X X where one of the x's is a 2 and the others are all 1s.
There are 6 ways to now slot in the 3.
Than makes 5*6 = 30 ways to have a 2, a 3 and four ones.
30+6 - 36 possibilities.
I think that is correct.
