Browse Questions

# How many chords can be drawn through 21 points on a circle?

$\begin{array}{1 1}(A)\;200\\(B)\;205\\(C)\;210\\(D)\;215\end{array}$

We get a chord by joining two points.If P is the number of chords from 21 points then,
$P=C(21,2)=\large\frac{21!}{2!(21-2)!}$
$\Rightarrow \large\frac{21!}{2!19!}$
$\Rightarrow \large\frac{21\times 20(19!)}{2\times 1(19!)}$
$\Rightarrow 21\times 10$
$\Rightarrow 210$ chords
Hence (C) is the correct answer.