When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers (i.e., 1, 2, 3, 4, 5, and 6) is

Let $P$ be the partial order defined on the set {1,2,3,4} as follows:

$P = \{(x, x) \mid x \in \{1,2,3,4\}\} \cup \{(1,2), (3,2), (3,4)\}$

The number of total orders on {1,2,3,4} that contain $P$ is _________.

Let $ x $ and $ y $ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let $ z = xy $ and let the mean values of $ x, y, z $ be $ \bar{x} , \bar{y} , \bar{z} $, respectively. Which one of the following statements is TRUE?

Let A be an n × n matrix over the set of all real numbers ℝ. Let B be a matrix obtained from A by swapping two rows. Which of the following statements is/are TRUE?