Out of thirty points in a plane, eight of them are collinear. The number of straight lines that can be formed by joining these points, is

Question

Out of thirty points in a plane, eight of them are collinear. The number of straight lines that can be formed by joining these points, is (A) 296 (B) 540 (C) 408 (D) 348

Tardigrade Admin · Accepted Answer

Total number of points in a plane is 30 . Out of them, 8 points are collinear. ∴ Total number of straight lines formed = 30 C2- 8 C2+1 =(30 × 29/2)-(8 × 7/2 × 1)+1 =435-28+1=408

Q. Out of thirty points in a plane, eight of them are collinear. The number of straight lines that can be formed by joining these points, is

296

540

408

348

Total number of points in a plane is $30$ .
Out of them, $8$ points are collinear.
$∴$ Total number of straight lines formed
$=^{30} C_{2} -^{8} C_{2} + 1$
$= \frac{30 \times 29}{2} - \frac{8 \times 7}{2 \times 1} + 1$
$= 435 - 28 + 1 = 408$

Q. Out of thirty points in a plane, eight of them are collinear. The number of straight lines that can be formed by joining these points, is

296

540

408

348

Total number of points in a plane is 30. Out of them, 8 points are collinear. ∴ Total number of straight lines formed =30C2​−8C2​+1 =230×29​−2×18×7​+1 =435−28+1=408

Total number of points in a plane is $30$ .
Out of them, $8$ points are collinear.
$∴$ Total number of straight lines formed
$=^{30} C_{2} -^{8} C_{2} + 1$
$= \frac{30 \times 29}{2} - \frac{8 \times 7}{2 \times 1} + 1$
$= 435 - 28 + 1 = 408$