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Question

The number of straight lines that can be formed by joining 20 points no three of which are in the same straight line except 4 of them which are in the same line

A
183
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B
186
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C
197
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D
185
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Solution

The correct option is D 185
There are 20 points out of which 4 are in a straight line.

To form a straight line we need 2 points

There are 3 ways
(i) select both points from 1 16C2120

(ii) select one from 1 and one from 2
16C1×4C116×464

(iii) select both points from 2 in 2 whichever way we select we get
any one line since they are collinear.

Hence total no. of ways =120+64+1=185

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