Permutations And Combinations

Question
CBSEENMA11014206

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

Solution

Since 21 points lie on the circumference of a circle.
∴ All the 21 points are distinct and no three of them are collinear. Now, we know that one and only one line can be drawn through 2 distinct points.
∴  Numbers of straight lines formed by 21 points by taking 2 at a time
                                        space space space space space equals 21 straight C subscript 2 space equals space fraction numerator 21 factorial over denominator 2 factorial space 19 factorial end fraction equals space fraction numerator 21 cross times 20 cross times 19 factorial over denominator 2 cross times 1 cross times 19 factorial end fraction equals 210.
   Hence, the number of chords = 210.
                                 

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