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Question

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
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B
Triangles formed by joining them is 116
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C
Straight lines formed by joining them is 45
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D
Triangle formed by joining them is 120
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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 =61=5
So required number of lines =455=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
So required number of triangles =1204=116

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