How many (i) lines (ii) triangles can be drawn through 8 points on a circle?

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Solution

Number of points $= 8$
(a) Number of lines :
Number of end points $= 2$
Number of lines
$\Rightarrow^{8} C_{2} \Rightarrow \frac{8!}{6! \times 2!} \Rightarrow 28$
Therefore number of lines is $28$
(b) Number of triangles :
Number of edges $= 3$
Numbers of lines
$\Rightarrow^{8} C_{3} \Rightarrow \frac{8!}{3! \times 5!} \Rightarrow 56$
Hence number of Triangles is $56$

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How many (i) lines (ii) triangles can be drawn through 8 points on a circle?

Number of points =8(a) Number of lines : Number of end points =2Number of lines ⇒8C2⇒8!6!×2!⇒28Therefore number of lines is 28(b) Number of triangles : Number of edges =3Numbers of lines ⇒8C3⇒8!3!×5!⇒56Hence number of Triangles is 56