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 = ${ }^{21} \mathrm{C}_{2}=\frac{21 !}{2 !(21-2) !}=\frac{21 !}{2 ! 19 !}=\frac{21 \times 20}{2}=210$