Question 15 of 42beginner🔧 ApplyNumerical2 marks

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

Correct Answer

210 chords

Exercise: EXERCISE 6.4 | Q: 3 | (Chapter: 20)
For More Understanding

Explanation

The textbook provides a similar illustration with 7 points on a circle, stating that the number of chords equals the number of combinations of 7 different things taken 2 at a time. Applying the same logic to 21 points, we need to find combinations of 21 different things taken 2 at a time, which is calculated using the formula for combinations.

Solution Steps

  1. Step 1: A chord is formed by joining any two points on a circle. Therefore, the number of chords that can be drawn through 21 points equals the number of ways of selecting 2 points from 21 points.

  2. Step 2: Since the order of selection does not matter (joining point A to point B is the same chord as joining point B to point A), this is a combination problem.

  3. Step 3: Number of chords = 21C2=21!2!×19!=21×202×1=210^{21}C_2 = \frac{21!}{2! \times 19!} = \frac{21 \times 20}{2 \times 1} = 210

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