6. (11 marks) A standard deck of 52 cards is given. (a) One card is drawn, what is the probability that the card is red in color? (b) What is the probability that a hand of five cards in poker contains five red cards and the five cards are not "J", "Q" or "K"? (c) What is the probability that a hand of five cards in poker contains five cards of the same suit and the five cards are not "A"? 5 7. (7 marks) Prove by Mathematical Induction, or disprove, 41 144 is a multiple of 27, for all natural numbers a. 8. (5 marks) Prove, or disprove, that if m is odd, then m' is odd, where me N