Question

Out of 25 points in a plane, no 3 are in a straight line except 8 are collinear.How many straight lines can be formed?

Answer 1

Answer:

399

Step-by-step explanation:

From 15 points you can make 15c3 triangles which is equal to 455 .

But it will contain triangle made from 8 collinear points which doesn't exists so we have to subtract the number of triangles made from 8 collinear points. No of triangle made from 8 collinear points are 8c3=56.

Hence total number of triangles are 455–56=399.

Answer 2

273 straight lines can be formed if Out of 25 points in a plane, no 3 are in a straight line except 8 are collinear

Given :

• 25 points
• except 8 point being collinear , no 3 points are in straight line

To Find:

• Number of straight lines formed

Solution:

2 points out of 25 can be selected in ²⁵C₂ ways

²⁵C² = 25!/(23!.2!)

= 25 * 24   / ( 2 * 1)

= 25 * 12

= 300

2 points out of 8 collinear point can be selected in ⁸C₂ ways

⁸C₂ = 8!/(6!.2!)

= 8 * 7   / ( 2 * 1)

= 4 * 7  

= 28

But there will be only 1 line , instead of 28 lines as points are collinear and all 28 lines will be same.

So number of straight lines  = 300 - 28 + 1

= 273

273 straight lines can be formed.