How many triangles can be formed by joining any three of $9$ points when no three of them are collinear.

74

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87

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86

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84

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Solution

The correct option is D $84$
The total number of ways to form a triangle by $9$ points are given by,
$^{9} C_{3}$
$= \frac{9!}{6! \times 3!}$
$= \frac{9 \times 8 \times 7}{3 \times 2}$
$= 84$

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How many triangles can be formed by joining any three of 9 points when no three of them are collinear.

The correct option is D 84The total number of ways to form a triangle by 9 points are given by, 9C3 =9!6!×3!=9×8×73×2=84

How many triangles can be formed by joining any three of $9$ points when no three of them are collinear.

The correct option is D $84$
The total number of ways to form a triangle by $9$ points are given by,
$^{9} C_{3}$
$= \frac{9!}{6! \times 3!}$
$= \frac{9 \times 8 \times 7}{3 \times 2}$
$= 84$