$\frac{20!}{10!}$ is

$\frac{20*19*18.......*11*10!}{10!}=20*19*18.....*11$


20!/5! is

$\frac{20*19*18.........*6*5!}{5!}=20*19*18...........*7*6$



Now, whatever prime factors we have in Quantity A will be present in Quantity B as well. The only difference will be created by the extra numbers 10 × 9 × 8 × 7 × 6 in Quantity B.

But since we need to consider only prime factors hence, the prime factors of 10 will be 2 and 5 which is present in 20 as well.

Similarly, the prime factor of 9 which is 3 is present in 18 as well.

The prime factor of 8 which is 2 is present in 16, the prime factor of 7 is present in 14 and the prime factors of 6 which is 2 and 3 is present in 12 as well.

Thus, Quantity A and Quantity B will have same number of prime factors.
Ans. (C)