$X_1, X_2,\ldots,X_9$ are nine points on the circumference of circle $O$. Line segments are drawn connecting each pair of points. How many line segments are drawn?
+26379 Line segments are drawn ?
\(X_1, X_2,\ldots,X_9 \text{ are nine points on the circumference of circle } O. \\ \text{Line segments are drawn connecting each pair of points.}\\ \text{How many line segments are drawn? }\)
\(\begin{array}{|c|c|} \hline \text{Points on the circumference of circle} & \text{Line segments are drawn connecting each pair of points} \\ \hline 2 & 1 \\ 3 & 2 + 1 \\ 4 & 3 + 2 + 1 \\ 5 & 4 + 3 + 2 + 1 \\ 6 & 5 + 4 + 3 + 2 + 1 \\ 7 & 6 + 5 + 4 + 3 + 2 + 1 \\ 8 & 7 + 6 + 5 + 4 + 3 + 2 + 1 \\ 9 & 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 \\ \cdots & \cdots \\ \\ n & \frac { (n-1) + 1} {2} \cdot (n-1) = \mathbf{ \frac{n\cdot (n-1) } {2} } = \binom{n}{2}\\ n=9 & \mathbf{ \frac{9\cdot (9-1) } {2} } = \frac{9 \cdot 8 } {2} = 9\cdot 4 = \mathbf { 36 }\\ \hline \end{array}\)
36 line segments are drawn.
