#MathUnusual | Best trick for counting triangles in figures | Triangle counting

Hello friends, this is Mahesh Yovlikar and you are watching Next Gen Maths. If you have not subscribed my channel then please subscribe the channel and press the bell icon. Dots are placed at the intersection of a grid. Then how many triangles one can draw by joining these dots? Like 1, 2, 3. But it is difficult to calculate it manually. So what we can do? We can associate numbers to each dot. Like 1, 2, 3, 4, 5, 6, 7, 8, 9. Total 9 number of dots. Now we are going to use the property of triangle. A triangle can be formed by 3 non-linear dots. So the combination of 3 numbers from 1 to 9 will form a triangle. But note that this number should not be lie on a line. The total number of combination of 3 numbers from 1 to 9 is 9C3. That means 9 into 8 into 7 divided by 3 factorial which is 84. But this 84 numbers can include collinear dots and we have to identify those combination of collinear dots and separate it from 84. There is a 6 straight lines and 2 diagonals which are combination of 3 collinear dots. Like 1, 2, 3, 4, 5, 6, 7, 8, 9. These are the 3 horizontal lines. 1, 4, 7, 2, 5, 8, 3, 6, 9. These are the 3 vertical lines. And 1, 5, 9, 3, 5, 7 are 2 diagonals. That means total 8 numbers which are the combination of 3 collinear dots. So the number of triangles can draw by joining these dots are 84-8 equal to 76. In other words, 76 triangles one can draw by joining dots. Thanks for watching. For more videos, like, share, subscribe, press the bell icon of NextGenMaths.