If A1 A2 ...... A18 is a regular polygon, then number of ways in which a quadrilateral can be formed with the help of vertices of given polygon, such that no side of quadrilateral is a side of given polygon, is-

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GivenA1A2...... A18is a regular polygon,
The number of ways in which a quadrilateral can be formed with the help of vertices of given polygon, such that no side of quadrilateral is a side of given polygon, is-
Number of ways of forming quadrilateral=18c4
Number of ways of forming quadrilateral with one side common=18*14c2
Number of ways of forming quadrilateral with 2 sides common=18*13c1
Number of ways of forming quadrilateral with 3 sides common=18 ways
Sonumber of ways in which a quadrilateral can be formed with the help of vertices of given polygon, such that no side of quadrilateral is a side of given polygon, is
=18c4-18*14c2-18*13c1-18=1170 ways