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

Question:

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

Solution:

For drawing one chord on a circle, only 2 points are required.

To know the number of chords that can be drawn through the given 21 points on a circle, the number of combinations have to be counted.

Therefore, there will be as many chords as there are combinations of 21 points taken 2 at a time.

Thus, required number of chords = ${ }^{21} \mathrm{C}_{2}=\frac{21 !}{2 !(21-2) !}=\frac{21 !}{2 ! 19 !}=\frac{21 \times 20}{2}=210$

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