Question

a positive integer divisor of 12! is chosen at random. the probability that the divisor chosen is a perfect square can be expressed as m n , where m and n are relatively prime positive integers. what is m n?

Answer 1

There are 6 positive divisors of 12: 1, 2, 3, 4, 6, and 12. Of these, 1 and 4 are perfect squares. So the probability of choosing a perfect square divisor of 12 is 2/6, or 1/3.