How many quadrilaterals can be drawn by joining the vertices of a convex polygon of 20 sides so that the quadrilateral do not have any side common with the polygon??

it is 20c4(can also be written as c(20,4))-20*c(18,2)+17*19-18 

total no. of quadrilateral=c(20,4)

total no. of quadrilateral with one side commmon=20*c(18,2)

reason=let's fix one side then no. of ways to form a quadrilteral then no. of points left =18 to choose 2 so c(18,2) = no. of ways ... fixing 20 sides so multiply by 20

inthe similar way we can find with 2 side common and 3 side common...

i've used alternate +- sign because in the case we take one side common there will be cases in which both side common will come....

this is same as aUb=a+b-(a intersection b)

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