Question: 9. Two distinct numbers a and b are chosen randomly from the set {1, 2, ..., n}, n 2 4. Which of the following probabilities

9. Two distinct numbers a and b are chosen randomly from

9. Two distinct numbers a and b are chosen randomly from the set {1, 2, ..., n}, n 2 4. Which of the following probabilities is larger: (2') P(a2 b2 is divisible by 2) or P(a2 b2 is divisible by 3); (ii) P(a3 b3 is divisible by 2) or P(a3 b3 is divisible by 3) ? (Note: to avoid lengthy bookkeeping you may assume that n is a very large number.)

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