Probability and Prime Numbers

Question

What is the probability that a positive divisor of 8748 million is the product of exactly 20 non-distinct primes?

Answer 1

Hint: $8748$ million $= 8748 \times 10^6 = 2^8 \cdot 3^7 \cdot 5^6$, which has $8+7+6 = 21$ non-distinct prime factors. Now, simply count the number of ways to remove just one prime factor, count the number of divisors, and divide.