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  • There are 12 points in a plane out of which 3 are collinear on one straight line . If m is number of triangles formed using these points and n is number of straight lines formed using these&nb

There are 12 points in a plane out of which 3 are collinear on one straight line . If m is number of triangles formed using these points and n is number of straight lines formed using these points then m+n equals 

Option: 1

283


Option: 2

218 


Option: 3

223 


Option: 4

224 


Answers (1)

best_answer

As we have learned

There are n points in the plane such that no three of them are on the same straight line except m of them which are on same straight line, then the number of straight lines formed by joining them is/are ^{n}C_{2}-\ ^{m}C_{2}+1 and number triangles is/are ^{n}C_{3}-\ ^{m}C_{3}.

 

Now,

No. of triangles = m = ^{12}C_3 - ^3 C_3 = 219

No. of lines = ^{12}C_2 - ^3 C_2 + 1= 64

m + n = 283

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