Question

Please solve q 137?

Answer 1

`color(blue)(91)`

Explanation:

There are 14 lines. Two lines to make a triangle.
So we want the number of combinations of 14 lines taken 2 at a time:

`color(white)(0)^14C_2=(n!)/(r!(n-r)!)=(14*13*(12*11*.....*1))/(2*(12*11*......*1))`

`=(14*13*cancel((12*11*.....1)))/(2*cancel((12*11*......*1)))=182/2=91`