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Combination with Restrictions

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Question

There are $12$ points in a plane out of which $7$ are in a straight line. The number of straight lines formed by joining all these points is

A

45

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B

46

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C

47

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D

48

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Solution

The correct option is B $46$
Since all the points in a straight line will give rise to only 1 line
Required number of straight line is $=^{12} C_{2} -^{7} C_{2} + 1 = 66 - 21 + 1 = 46$

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