Catherine rolls a standard 6-sided die six times. If the product of her rolls is 600 then how many different sequences of rolls could there have been? (The order of the rolls matters.)

Answer 1

We need to find all the possible sequences of 6 rolls that result in a product of 600.

Since $600= 2^3 * 3 * 5^2$, we need to find sequences of 6 rolls that multiply to this factorization.

There are 6 possible sequences for the 3 2's: (2, 2, 2), (4, 2), (2, 4), (3, 2, 2), (2, 3, 2), (2, 2, 3)

There are 2 possible sequences for the 3: (3, 5), (5, 3)

There are 2 possible sequences for the 5's: (5, 5), (6, 5)

Therefore, there are a total of $6 * 2 * 2 = 24$ different sequences of rolls that could result in a product of 600.