IOPC14A ; small doubt

iopc14a

#1

given a=n! and b as stated in the question http://www.codechef.com/problems/IOPC14A .Isnt it enough to just find (n!/b)%2 and this can be written as (n!)%2 * (b^(2-2))%2 =(n!)%2

am i wrong in assuming something because i m using fermet’s little theorm