Question

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

How many different 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?

Answer 1

There are 62 different possible sequences if you roll the dice twice.

Hint: The probability of getting a sequence of 10 even numbers is 310/610.

Hint: If the first, third, and fourth numbers must be the same, there are 6∗6n possible sequences, where n is the number of non-fixed dice.