do not have the same letter at the beginning and end of the word?
I would like to use the Difference Rule: All the permutations - permutations with the same letter at the beginning and end(P......P;O.....O;S......S) = $\binom {14}{1,1,3,2,1,1,1,1,1,2}$-$\binom{12}{1,1,1,2,1,1,1,1,1,2}$-2$\binom{12}{1,1,3,1,1,1,1,1,2}$
The correct answer I was given is 199,584,000
It seems like I forgot to minus something else, can some one help me with this? Thank you!