Let
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
be a positive integer. Consider words of length
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
composed of letters from the set
![\{ M, E, O \}](/media/m/8/5/3/853d6ecb665bf9929d86a49596ce78da.png)
. Let
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
be the number of such words containing an even number (possibly 0) of blocks
![ME](/media/m/0/9/f/09fe7f54e93fe547123cecfc182bc6e2.png)
and an even number (possibly 0) blocks of
![MO](/media/m/4/b/3/4b3f6143964c0f904266b94364775916.png)
. Similarly let
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
the number of such words containing an odd number of blocks
![ME](/media/m/0/9/f/09fe7f54e93fe547123cecfc182bc6e2.png)
and an odd number of blocks
![MO](/media/m/4/b/3/4b3f6143964c0f904266b94364775916.png)
. Prove that
![a>b](/media/m/9/3/e/93ec187b4eea9a155615a5025c8701f3.png)
.
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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 $a>b$.