Random divisor of 20 factorial being a multiple of 20

A divisor of $20!$ is chosen uniformly at random from all of its positive divisors. What is the probability that the chosen divisor is a multiple of $20$?

$\tfrac{68}{95}$. Since $20!=2^{18}3^8 5^4\cdots$, a divisor picks each prime exponent independently and uniformly. It is a multiple of $20=2^2\cdot5$ when the exponent of 2 is at least 2 ($\tfrac{17}{19}$) and of 5 at least 1 ($\tfrac45$), giving $\tfrac{68}{95}$.