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 \[ E \alpha \frac {1}{n^2} \] 

 \[ \Omega (n=1) = 1 \] 

 \[ \Omega (n=2) = 4 \] 

 \[ \sum_v a_v E_v = \epsilon \] 

 \[ w (\overline{a}) = \frac{ A! }{ a_1! a_2! a_3! ..... a_v! } \] 

 \[ w (\overline{a}) = \frac{ A! }{ \Pi_v a_v!} \] 

 \[ a_1 \] 

 \[ \mbox{Number of systems in state 1} \] 

 \[ a_{\nu} \] 

 \[ \mbox{Number of systems in state v} \] 

 \[ P_v = \frac{1}{A} \frac{ \sum_{\overline {a}} \omega (\overline{a}) a_v (\overline{a} ) }{ \sum_{\overline a} \omega (\overline{a}) } \] 

 \[ w(A) = \frac{4!}{0!4!} \] 

 \[ w(A) = 1 \] 

 \[ \mbox{Distribution B} \] 

 \[ w(B) = \frac{4!}{1!3!} \] 

 \[ w(B) = 4P_1 = \frac{1}{4} \left ( \frac{1 \cdot 0 + 4 \cdot 1 + 6 \cdot 2 + 4 \cdot 3 + 1 \cdot 4}{1 + 4 + 6 + 4 + 1} \right ) \] 

 \[ P_1 = \frac{1}{2} \] 

 \[ w(a) \]