When n balls, numbered 1, 2, 3,.... n are taken in succession from a container, a rencontre occurs if the mth ball withdrawn is numbered m, for some 1 ≤ m ≤ n. Find the probability of getting (i) no rencontres; (ii) (exactly) one rencontre, (iii) at least one rencontre; and (iv) r rencontres, where 1 ≤ r ≤ n. b) Approximate the answers to the questions in part (a)