Question 40
Let $m$ be a positive integer and let $A$, respectively $B$, be an alphabet with $m$, respectively $2m$ letters. Let $n$ be an even integer greater than or equal to $2m$. Let $a_n$ be the number of words of length $n$ made of letters from $A$ such that every letter in $A$ occurs a positive even number of times. Let $b_n$ be the number of words of length $n$ made of letters from $B$ such that every letter in $B$ occurs an odd number of times. Determine the ratio $b_n/a_n$.