Question 1210203
Let's break down this problem step by step.

**1. Prime Factorization of 20^20**

* 20 = 2² * 5
* 20²⁰ = (2² * 5)²⁰ = 2⁴⁰ * 5²⁰

**2. Number of Divisors**

The number of divisors of 20²⁰ is found by adding 1 to each exponent in the prime factorization and multiplying them:

* Number of divisors = (40 + 1) * (20 + 1) = 41 * 21 = 861

**3. Divisors that are Multiples of 5**

For a divisor to be a multiple of 5, it must have at least one factor of 5.

* The form of a divisor of 20²⁰ is 2^a * 5^b, where 0 ≤ a ≤ 40 and 0 ≤ b ≤ 20.
* For a multiple of 5, we need b ≥ 1, so 1 ≤ b ≤ 20.
* The number of choices for 'a' is still 41 (0 to 40).
* The number of choices for 'b' is 20 (1 to 20).
* Number of multiples of 5 = 41 * 20 = 820

**4. Calculate the Probability**

* Probability = (Number of multiples of 5) / (Total number of divisors)
* Probability = 820 / 861

**5. Simplify the Fraction**

We can simplify the fraction by dividing both numerator and denominator by their greatest common divisor.

* 820 = 2² * 5 * 41
* 861 = 3 * 7 * 41

The greatest common divisor is 41.

* Probability = (820 / 41) / (861 / 41)
* Probability = 20 / 21

**Therefore, the probability that we chose a multiple of 5 is 20/21.**