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

maximum log-likelihood estimation problem is to find:

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

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

(Hint: You have no control overx1,...,xkornand 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