If p and q are prime numbers, how many divisors does the product p^3 * q^7 have?  Choose the correct choice from the following answers:
A) 25
B) 30
C) 32
D) 35
E) 40

Rationale: "when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is c . 4 * 8 = 32"
Answer: C