# A fair 6-sided die is rolled 10 times and the resulting sequence of 10 numbers is recorded, how many sequences are possible?

A fair 6-sided die is rolled 10 times and the resulting sequence of 10 numbers is recorded,

How many sequences are possible? How many different sequences consist entirely of even numbers? How many different sequences are possible if the first, third, and fourth numbers must be the same?

-
What have you tried? Any thoughts? For starters, how many sequences of length 2 are possible? You can count those by hand. –  Ross Millikan Mar 13 '13 at 19:59
Hint: There are $6^{2}$ different possible sequences if you roll the dice twice.
Hint: The probability of getting a sequence of 10 even numbers is $3^{10}/6^{10}$.
Hint: If the first, third, and fourth numbers must be the same, there are $6 * 6^{n}$ possible sequences, where $n$ is the number of non-fixed dice.