We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen). What is the probability that we chose a multiple of 10^{20}? Express your answer as a fraction in simplest form.
[20^20] / [10^20] ==1,048,576 ==2^20 ==which has 20 + 1 ==21 divisors.
20^20 ==1.048576e+26 = 2^40 * 5^20 ==41 * 21 ==861 divisors.
The probability is: 21 / 861 == 1 / 41
