How many triangles can be obtained by joining 12 points, five of … - Vidyadip

Question

How many triangles can be obtained by joining 12 points, five of which are collinear?

✓

Answer

We have,
Since 5 out of 12 points are collinear, So the number of triangle will be,
$={^{12}{\text{C}}}_{\text{3}}-{^{5}{\text{C}}}_{\text{3}}$
$=\frac{12!}{3!9!}-\frac{5!}{3!2!}$
$=\frac{12\times11\times10}{3\times2}-\frac{5\times4}{2}$
$=220-10$
$=210$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Combinations→Combinations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The base of an equilateral triangle with side 2a lies along the they-axis such that the mid-point of the base is at the origin. Find the vertices of the triangle.

Prove that:
$\sin6\circ\sin42^\circ\sin66^\circ\sin78^\circ=\frac{1}{16}$

A man saved ₹ 66000 in 20 years. In each succeeding year after the first year he saved ₹ 200 more than what he saved in the previous year. How much did he save in the first year?

In how many ways can one select a circket team of eleven from17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?

$\text{If}\ \frac{\cos(\text{A}-\text{B})}{\cos(\text{A+B})}+\frac{\cos(\text{C+D})}{\cos(\text{C}-\text{D})}=0,$ prove that $\tan\text{A}\tan\text{B}\tan\text{C}\tan\text{D}=-1$

Using distance formula prove that the following points are collinear:
A(4, -3, -1), B(5, -7, 6) and C(3, 1, -8)

Find the equations of the circles touching $y-$axis at $(0, 3)$ and making an intercept of $8$ units on the $x-$axis.

The mean and standard deviation of a set of $n_1$ observations are $\bar{\text{x}}_1$ and $S_1,$ respectively while the mean and standard deviation of another set of $n_2$ observations are $\bar{\text{x}}_2$ and $S_2,$ respectively. Show that the standard deviation of the combined set of $(n_1 + n_2 )$ observations is given by $\text{S.D.}=\sqrt{\frac{\text{n}_1(\text{s}_1)^2+\text{n}_2(\text{s}_2)^2}{\text{n}_1+\text{n}_2}+\frac{\text{n}_1\text{n}_2(\bar{\text{x}}_1-\bar{\text{x}}_2)^2}{(\text{n}_1+\text{n}_2)^2}}$

Differentiate the following from first principle$\tan\sqrt{\text{x}}$

Find the lines through the point $(0, 2)$ making angles $\frac{\pi}{3}$ and $\frac{2\pi}{3}$ with the $x-$axis. Also, find the lines parallel to them cutting the $y-$axis at a distance of $2$ units below the origin.