There are 25 points in a plane, of which 10 are on the same line. Of the rest, no three are collinear and no two are collinear with any one of the first ten points. The number of different straight lines that can be formed by joining these points is

Question

There are 25 points in a plane, of which 10 are on the same line. Of the rest, no three are collinear and no two are collinear with any one of the first ten points. The number of different straight lines that can be formed by joining these points is (A) 256 (B) 106 (C) 255 (D) 2105

Tardigrade Admin · Accepted Answer

Out of 25 given points, 10 are collinear and hence they form only one straight line. Out of rest of the 15 points, we have 15C2 straight lines and any one point out of these 15 points with any one of 10 collinear points forms a straight line. Hence, total straight lines formed = 15C2 + 15C1× 10C1 + 1 = 256.

Q. There are $25$ points in a plane, of which $10$ are on the same line. Of the rest, no three are collinear and no two are collinear with any one of the first ten points. The number of different straight lines that can be formed by joining these points is

$256$

$106$

$255$

$2105$

Q. There are 25 points in a plane, of which 10 are on the same line. Of the rest, no three are collinear and no two are collinear with any one of the first ten points. The number of different straight lines that can be formed by joining these points is

256

106

255

2105

Q. There are $25$ points in a plane, of which $10$ are on the same line. Of the rest, no three are collinear and no two are collinear with any one of the first ten points. The number of different straight lines that can be formed by joining these points is

$256$

$106$

$255$

$2105$