# Number of different substitution alphabet ciphers possible with given conditions?

If you consider a 26 letter alphabet, and a cipher where 24 of the letters are sent to themselves, and only 2 letters switch, how many different substitution alphabet ciphers are there, and what percentage are they of total possible?

I thought it would be there are $26\cdot25=650$ such possible ciphers, for a percentage of $$\frac{26\cdot25}{26!}\cdot100\approx1.61\cdot10^{-22}\%$$

But it seems there are only $325$ possible ciphers, when switching only two letters, and i dont understand why?

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Hint: Try that calculation with a 2 letter alphabet where 0 of the letters are sent to themselves. $\hspace{.79 in}$ – Ricky Demer Jun 2 '14 at 23:38
If $\Sigma=\{a,b\}$ then wouldnt you have only one possible cipher combination? I feel like something should have clicked from that, but it didnt nor as i try to think of smaller cases now... – Finding Nemo 2 is happening. Jun 3 '14 at 1:13