Maps $g$ maps $\left\{1,2,3,4,5\right\}$ onto $\left\{11,12,13,14\right\}$ and $g(1)\neq g(2)$. How many g are there.
My answer: I transformed the question to a easy-understand way and find out the solution. Consider there are five children and four seats. Two of them are willing sitting together but only two of them never seat together.
$\left(\begin{pmatrix} 5 \\ 2 \end{pmatrix}-1\right)*4!=456$
However the answer is 216. I don't know what's wrong.
Could you please help me find out what's wrong or give a right way to solve the problem?
Thanks!