Question

Regular 201 -sided polygon is inscribed inside a circle of centre 'N' . Triangles are drawn by connecting any three of the 201 vertices of the polygon. The number of triangles have the point Lying inside the triangle is 'N' , then find sum of digits of 'C' .​

Answer 1

Step-by-step explanation:

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Answer 2

Given :- Regular 201 sided polygon is inscribed inside a circle of centre 'N' . Triangles are drawn by connecting any three of the 201 vertices of the polygon. The number of triangles have the point Lying inside the triangle is 'C' , then find sum of digits of 'C' .

Answer :-

we have,

→ Total sides of polygon = 201 .

and,

→ Triangle has sides = 3 .

so,

→ Total number of triangles formed will be = (201) C (3) = 201 ! / {(201 - 3)! * 3!} = (201 * 200 * 199 * 198!) / (198! * 3!) = (201 * 200 * 199)/(3 * 2 * 1) = 67 * 100 * 199 = 1333300 .

then,

→ C = 1333300

therefore,

→ Sum of digits of C = 1 + 3 + 3 + 3 + 3 + 0 + 0 = 13 (Ans.)

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