Pascal's coefficient identity

0th row:11st row:112nd row:1213rd row:13314th row:14641   \begin{array}{rc} 0^\text{th} \text{ row:} & 1 \\ 1^\text{st} \text{ row:} & 1 \quad 1 \\ 2^\text{nd} \text{ row:} & 1 \quad 2 \quad 1 \\ 3^\text{rd} \text{ row:} & 1 \quad 3 \quad 3 \quad 1 \\ 4^\text{th} \text{ row:} & 1 \quad 4 \quad 6 \quad 4 \quad 1 \\ \vdots \ \ \ & \cdot \quad \cdot \quad \cdot \quad \cdot \quad \cdot \quad \cdot \end{array}

Pascal's triangle is shown above for the 0th0^\text{th} row through the 4th4^\text{th} row. What is the 4th4^\text{th} element in the 10th10^\text{th} row?


Note: Each row starts with the 0th0^\text{th} element. For example, the 0th0^\text{th}, 1st1^\text{st}, 2nd2^\text{nd}, and 3rd3^\text{rd} elements of the 3rd3^\text{rd} row are 1, 3, 3, and 1, respectively.

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