need help with some discrete mathematics questions. this is in discrete mathematics subject

here are the questions i need help with:

Problem 7

You got six dice for your birthday, and feel obligated to actually use them. So you are playing around with them and starting to do some probability computations about the outcomes of rolling all six dice at the same time.

a) What is the probability that all of the six dice show the number five?

b) What is the probability that all six dice show the same number?

c) What is the probability that no two dice show the same number, i.e., that you roll the numbers 1, 2, 3, 4, 5, and 6?

d) What is the probability that two of the dice show the number six and the other four show the number three?

e) What are the expected value and the standard deviation of the sum of the six numbers that you roll?

problem 8

Someone plays a prank on you and loads your six dice so that now each of them shows the number 3 twice as often as the other numbers. The other numbers are still equally likely to occur.

a) What is the probability that all of the six dice show the number five?

b) What is the probability that all six dice show the same number?

c) What is the probability that no two dice show the same number, i.e., that you roll the numbers 1, 2, 3, 4, 5, and 6?

d) What is the probability that two of the dice show the number six and the other four show the number three?

problem 9

a) An urn contains four red balls and four blue balls. You draw two balls from the urn, one after the other, without putting them back. Event A is that the first ball is red, and event B is that the second ball is red. Are events A and B independent? Prove your answer.

b) This time you are using the same urn and balls, but you draw three balls, again one after the other. Event C is that the first two balls you draw have the same color, and Event D is that the third ball is red. Are events C and D independent? Again, prove your answer.

e) What are the expected value and the standard deviation of the sum of the six numbers that you roll?