$\displaystyle

\left(\begin{array}{cc}n\\n_{1},n_{2}, ..., n_{k}\end{array}\right) = \frac{n!}{n_{1}!n_{2}!...n_{k}!}

$

$\displaystyle

P(X=k) = \frac{1}{n}

$

$\displaystyle

E(X) = \frac{n+1}{2}

$

$\displaystyle

V(X) = \frac{n^{2}-1}{12}

$

$\displaystyle

= \frac{P(A_{i}) \times P(E \mid A_{i})}{P(A_{1}) \times P(E \mid A_{1}) + P(A_{2}) \times P(E \mid A_{2}) + ... + P(A_{n}) \times P(E \mid A_{n})}

$