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Moving only south and east along the line segments, how many paths are there from A to B?

$\begin{array}{|rcll|} \hline && {^{12}}C_3- {^5}C_1 {^6}C_1- {^6}C_1 {^5}C_1 \\ &=& {^{12}}C_3-2\cdot {^5}C_1{^6}C_1 \\ &=& 220-2\cdot 30 \\ &=& 220-60 \\ &=& 160 \\ \hline \end{array}$