Three distinct integers are chosen at random from the set {1, 2, ..., 15}. Find the probability that: (i) Their sum is odd. (ii) Their product is odd. (iii) The sum is odd if it is known that product is odd. (iv) The product is odd if it is known that the sum is odd. (v) Answer questions (i)–(iv) if three integers are selected from {1, ..., 20}. (vi)

Generalize answers to (i)–(iv) in the case of selection from {1, ...,n}. (vii) Answer questions (i)–(iv) by drawing from {1, ...,n}, and passing to the limit with n → ∞.