Counting words!
Source: Romania TST 2014 Day 5 Problem 2
January 21, 2015
functioncombinatorics unsolvedcombinatorics
Problem Statement
Let be a positive integer and let , respectively , be two alphabets with , respectively letters. Let also be an even integer which is at least . Let be the number of words of length , formed with letters from , in which appear all the letters from , each an even number of times. Let be the number of words of length , formed with letters from , in which appear all the letters from , each an odd number of times. Compute .