Afair 6-sided die is rolled 8 times and the resulting sequence of 8 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?

a) 1,679,616 sequences

b) 6,561 sequences

c) 46,656 sequences

Step-by-step explanation:

a) How many different sequences are possible?

For each of the 8 dice, there are 6 possible outcomes. Therefore, the total number of difference sequences is:

b) How many different sequences consist entirely of even numbers?

For each of the 8 dice, there are 3 possible even outcomes. Therefore, the total number of difference sequences is:

c) How many different sequences are possible if the first, third, and fourth numbers must be the same?

If the first, third and fourth numbers are fixed, there are only 5 "free" positions, while there are 6 possible outcomes for the fixed positions since they have to be the same

days of the week

step-by-step explanation:

javier earned more money then kyle, so that won't always be a constant term, but the days of the week do not change so that term is always constant.

edit: i meant