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A regular polygon has 20 sides. How many triangles can be draw

Question

A regular polygon has $20$ sides. How many triangles can be drawn by using the vertices but not using the sides $?$

800

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Lucas Discussed

A regular polygon has

20

sides. How many triangles can be drawn by using the vertices but not using the sides

?

15 mins ago

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15 mins ago

Text solutionVerified

The first vertex can be selected in

20

ways. The remaining two are to be selected from

17

vertices so that they are not consecutive. This can be done in

^{17} C_{2} - 16

ways. The total number of ways

= 20 \times (^{17} C_{2} - 16)

But in this method, each selection is repeated thrice.
Number of triangles

= \frac{20 \times ( ^{17} C _{2} - 16 )}{3} = 800.

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Question Text	A regular polygon has $20$ sides. How many triangles can be drawn by using the vertices but not using the sides $?$
Answer Type	Text solution:1
Upvotes	150