Two integers x and y are chosen with replacement from the set [0, 1, 2, ........., 10]. The probability that | x $$-$$ y | > 5 is

Three dice having digits 1, 2, 3, 4, 5 and 6 on their faces are marked I, II, and III and rolled. Let x, y and z represent the number on die-I, die-II and die-III, respectively. What is the number of possible outcomes such that x > y > z ?

In a binomial distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials ?

Consider the following statements

I. P($$\overline A $$ $$\cup$$ B) = P($$\overline A $$) + P(B) $$-$$ P($$\overline A $$ $$\cap$$ B)

II. P(A $$\cap$$ $$\overline B $$) = P(B) $$-$$ P(A $$\cap$$ B)

III. P(A $$\cap$$ B) = P(B) P(A / B)

Which of the above statements are correct?