Conceptually all options are correct
Because Big Oh means f(n) = O(g(n)) f(n) is less than or equal to g(n)
look first of all n! = n*(n-1)*(n-2)*..........*1 < n*n*n*........
so NN can be upper bound to n!
2nd is log(n!) = log(n*(n-1)*(n-2)*..........*1) < log(n*n*n*........)
and log(nn) = n*logn which can be a upper bound to log(n!)