How many different Strings can I create with the characters of the String *SPEISESTAERKE*? How many different Strings can I create with the characters of the String SPEISESTAERKE ?
According to that post, I have tried the following. Note, that I use all the given characters at once to create all possible combinations: 
$2 \times$S, 
$1 \times$P, 
$4 \times$E,
$1 \times$I,
$1 \times$A,
$1 \times$R,
$1 \times$K
$\binom {13}{2} \cdot \binom {11}{1} \cdot \binom {10}{4} \cdot \binom {6}{1} \cdot \binom {5}{1} \cdot \binom {4}{1} \cdot \binom {3}{1} \cdot \binom {2}{1} \cdot \binom {1}{1} = 129 729 600$
Unfortunately this is the wrong answer. The correct solution is $432 432 00$.
Question: How can I achieve the correct result?

alternative answer - with correctly counted letters: 
$\binom {13}{3} \cdot \binom {10}{4} \cdot \binom {6}{1} \cdot \binom {5}{1} \cdot \binom {4}{1} \cdot \binom {3}{1} \cdot \binom {2}{1} \cdot \binom {1}{1}  = 432 432 00$
