Summing The Triangle

Probability Level 1

111121133114641 \begin{array}{c} 1 \end{array} \\ \begin{array}{cc} 1 & 1 \end{array} \\ \begin{array}{ccc} 1 & 2 & 1 \end{array} \\ \begin{array}{cccc} 1 & 3 & 3 & 1\end{array} \\ \begin{array}{ccccc} 1 & 4 & 6 & 4 & 1\end{array} \\ \begin{array}{cccccc} \vdots & \hphantom{\vdots} & \vdots & \hphantom{\vdots} & \vdots \end{array} \\

Pascal's triangle is shown above for the 0th0^\text{th} row through the 4th4^\text{th} row.

What is the sum of all the elements in the 12th12^\text{th} row?


Note: The topmost row in Pascal's triangle is the 0th0^\text{th} row. Then, the next row down is the 1st1^\text{st} row, and so on.

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