Question

R sided polygons are formed by joining the vertices of an n sided polygon

Answer 1

Answer:

Step-by-step explanation:

Our question is R sided polygons are formed by joining the vertices of an n sided polygon.

Hence we need to consider various conditions on ever point since it is c^1(R) in order to find how many polygons.

y1 − y2 ≥ 0

y2 − y3 ... y(r−1) ≥ 1

y1 + y2 + y3 .... y(r−1) ≥ 1

y1 + y2 + y3 .... yr = N−2r

= N − 2r + r − 1(C(r−1)) = N − r − 1(C(r−1))

Thus, the number of polygons is equal to N, which is the same as:

N − r − 1(C)(r−1) + N − r(Cr).

Hence, proved.

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