There are 10 points in a plane out of these points no three are in the same straight line except 4 points which are collinear. How many
(i) straight lines
(ii) trian-gles
(iii) quadrilateral, by joining them?

Explanation

(i) Required number of straight lines
`=.^(10)C_(2)-.^(4)C_(2)+1=(10*9)/(1*2)-(4*3)/(1*2)+1=45-6+1=40`
(ii) Required number of triangles
`=.^(10)C_(3)-.^(4)C_(3)=(10*9*8)/(1*2*3)-.^(4)C_(1)=120-4=116`
(iii) Required number of quadrilaterals
`=.^(10)C_(4)-(.^(4)C_(3).^(4)C_(1)+.^(4)C_(4).^(6)C_(0))`
`=(10*9*8*7)/(1*2*3*4)-(.^(4)C_(1)*.^(6)C_(1)+1.1)`
`=210-(4xx6+1)=210-25=185`