MEMO 2012 T3

Let $n$ be a positive integer. Consider words of length $n$ composed of letters from the set $\{ M, E, O \}$ . Let $a$ be the number of such words containing an even number (possibly 0) of blocks $ME$ and an even number (possibly 0) blocks of $MO$ . Similarly let $b$ the number of such words containing an odd number of blocks $ME$ and an odd number of blocks $MO$ . Prove that $a>b$ .