# Pascal's hockey shot

Probability Level 1

$\begin{array}{c} 1 \end{array} \\ \begin{array}{cc} 1 & 1 \end{array} \\ \begin{array}{ccc} 1 & 2 & \color{#D61F06}{1}\end{array} \\ \begin{array}{cccc} 1 & 3 & \color{#D61F06}{3} & 1\end{array} \\ \begin{array}{ccccc} 1 & 4 & \color{#D61F06}{6} & 4 & 1\end{array} \\ \begin{array}{cccccc} \vdots & \hphantom{\vdots} & \vdots & \hphantom{\vdots} & \vdots \end{array}\\ \begin{array}{cccccc} 1 & 25 & \color{#D61F06}{300} & 2300 & 12650 & \cdots \end{array} \\ \begin{array}{ccccccc} 1 & 26 & 325 & 2600 & 14950 & \cdots & \hphantom{1000} \end{array} \\$

Pascal's triangle is shown above for the $0^\text{th}$ row through the $4^\text{th}$ row, and parts of the $25^\text{th}$ and $26^\text{th}$ rows are also shown above.

What is the sum of all the $2^\text{nd}$ elements of each row up to the $25^\text{th}$ row?


Note: The visible elements to be summed are highlighted in red.

Additional clarification: The topmost row in Pascal's triangle is the $0^\text{th}$ row. Then, the next row down is the $1^\text{st}$ row, and so on. The leftmost element in each row of Pascal's triangle is the $0^\text{th}$ element. Then, the element to the right of that is the $1^\text{st}$ element in that row, and so on.

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