+748 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.)
+130 6 can be written with 6 dice in 2 ways:
6 * 1 * 1 * 1 * 1 * 1
2 * 3 * 1 * 1 * 1* 1
The first one has 6 ways to write it (6 spots for the 6 to go into)
The second one has 6 * 5 = 30 ways to write it (6 spots for the 3, 5 spots for the 2)
Therefore, there are 6 + 30 = 36 sequences of rolls
