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

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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step-by-step explanation: