no. of zeroes in ²⁰⁰²C₁₀₀₁

There's a formula for finding the power of a prime p in n!.

If n!=p^a.q^br^c...

Then

(where [.] represents greatest integer function)

similarly for q,b and r,c and all other prime factors of n!..

To find no. of zeroes in ²⁰⁰²C₁₀₀₁, you must know power of 5 in 2002! and 1001! since

²⁰⁰²C₁₀₀₁

So simply find the power of 5 and that will give you the no. of zeroes...