K non-intersecting diagonals in a polygon

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Given a regular N-sided polygon, how many ways can you draw K non-intersecting diagonals? Any pair of diagonals must not intersect strictly inside the polygon.


For e.g. N = 4 and K = 2 -> 2 ways

Quadrilateral polygon and 2 non intersecting diagonals


N = 5 and K = 2 -> 5 ways Pentagon and 2 non intersecting diagonals


N = 5 and K = 3 -> 0 ways