# Pascal's coefficient identity

Probability Level 1

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

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


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

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