Given the sets S = {12, 8, 7, 5, 2, 1}, T = {9, 2, 8, 1, 3}, and U = {x | x is an integer and 1 x 12}, what are the following sets?

S T

S T

S U

S T

S

T

U

Given n = 6 and k = 3, compute the following:

The number of permutations of k of n objects.

The number of combinations of k of n objects.

For the following questions, assume that you have fair, six-sided dice:

If you roll a single die, what is the probability of rolling a 3?

What is the probability of rolling a 2 or a 4?

Assuming the value function f (ei) returns the number rolled for a given outcome (in other words, the function return a value from 1 to 6), what is the expected value of rolling a single die?

There are 36 possible outcomes for rolling two dice (6 outcomes for the first die times 6 outcomes for the second die.) What is the probability of both dice coming up with the different number?