How many triangles can be formed from 12 points out of which 7 of them are always collinear?

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

Answer : Total number of points on plane = 12 Triangles can be formed from these points = 12C3

= 220

But 4 points are colinear, the number of triangles can be formed from these points

= 4C3

= 4

We need to subtract 4 from 220 because in the formation of triangles from 4 colinear points are added there.

So no of triangle formed is = 220 – 4

= 216

There are 12 distinct non-collinear points in a same plane, they are points A,B,....L.

How many different triangle can be formed, with criteria one of its vertice must be contain point A?

My attempt:

Because the arrangements didn't need an order, so we can use combination to solve this problem.

Since there are 12 points and we need only to take three of them, so the possibility is

C(12,3) = 220

If there is no criteria, I think this is the total number to create the triangle from the 12 distinct points.

But, how about the numbers of solution if the criteria is required one of its vertice must be point A? Is the total possibility remains the same?

Thanks

IBPS Mains Admit Card has been released on 29th September 2022. The candidates who are qualified in the Prelims are eligible to attend the Mains examination. The mains exam is going to be held on 8th October 2022. Earlier, the IBPS Clerk Prelims Result was released on 21st September 2022. The selection process for the IBPS Clerk exam consists of two stages - Prelims & Mains exam. A total number of 6035 vacancies are available for the IBPS Clerk recruitment. The finally appointed candidates will be entitled to a pay scale of INR 11,765 to INR 31,540.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!