(x1,..., xk; n, p1,..., pk) := log (n! / x1!..xk!) p1^x1 ....pxk^xk

maximum log-likelihood estimation problem is to find:

arg max log
p(x1,..., xk; n; p1,..., pk)

over all possible choices of (
p1,..., pk) such that sum of all pi = 1.

(Hint: You have no control over x1,..., xk or n and may regard them as given.)

Well I know that I need to find first derivative of function p, and of function "g"- constraint, but I don't know where, or how to actually start...

Please help, thank you