2012 AMC 10B Problems/Problem 22

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Problem 22

Let ($a1$, $a2$, ... $a10$) be a list of the first 10 positive integers such that for each $2\le$i$\le10$ either $ai + 1$ or $ai-1$ or both appear somewhere before $ai$ in the list. How many such lists are there?


$\textbf{(A)}\ \120\qquad\textbf{(B)}\512\qquad\textbf{(C)}\ \1024\qquad\textbf{(D)}\ 181,440\qquad\textbf{(E)}\ \362,880$ (Error compiling LaTeX. Unknown error_msg)