There are 10 points in a plane, no three of which are in the same straight line excepting 4, which are collinear. Then number of
A
Straight lines formed by joining them is 40
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
Triangles formed by joining them is 116
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Straight lines formed by joining them is 45
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Triangle formed by joining them is 120
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct options are A Straight lines formed by joining them is 40 B Triangles formed by joining them is 116 We know that joining of any 2 points give a line. Thus the number of lines obtained from 10 points, when no 3 of which are collinear =10C2=45
Lines obtained from 4 points =4C2=6
No of lines lost due to 4 collinear points =6−1=5
So required number of lines =45−5=40
Also we know that any triangle can be obtained by joining any 3 points not in the same straight line. Thus number of triangles obtained from 10 different point, no 3 of which are collinear are =10C3=120
Triangles obtained from 4 points =4C3=4
Number of triangles lost due to 4 collinear points=4