Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many
(i) straight lines
fill triangles can be formed by joining them?

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Solution

18 points,5 collinear :
(a) No. of lines = $^{18} C_{2}$ - $^{5} C_{2}$ + 1 = 153 - 10 + 1 = 144
(b) No. of $Δ^{s}$ = $^{18} C_{3}$ - $^{5} C_{3}$ = 816 - 10 = 806.

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Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many(i) straight linesfill triangles can be formed by joining them?

18 points,5 collinear :(a) No. of lines = 18C2 - 5C2 + 1 = 153 - 10 + 1 = 144(b) No. of Δs = 18C3 - 5C3 = 816 - 10 = 806.

Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many
(i) straight lines
fill triangles can be formed by joining them?

18 points,5 collinear :
(a) No. of lines = $^{18} C_{2}$ - $^{5} C_{2}$ + 1 = 153 - 10 + 1 = 144
(b) No. of $Δ^{s}$ = $^{18} C_{3}$ - $^{5} C_{3}$ = 816 - 10 = 806.