Is the binomial coefficient (63)=6!3!⋅3!\binom{6}{3} = \frac{6!}{3! \cdot 3!}(36)=3!⋅3!6! divisible by 5?
Yes, and 525^252 divides it
Yes, but 525^252 does not divide it
No, 5 does not divide it
Cannot be determined