Question

Suppose there are 5 red points and 4 blue points on a circle Then the number of convex polygons whose vertices among the 9 points and having atleast one blue vertex is

Answer 1

Step-by-step explanation:

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Answer 2

The number of convex polygons having at least one blue vertex whose vertices are among the 9 points is 450.

Given:

There are 4 blue points and 5 red points on a circle.

To Find:

The number of convex polygons having at least one blue vertex whose vertices are among the 9 points is

Solution:

The total number of polygons is

$(\frac{9}{3}) + (\frac{9}{4}) +..........(\frac{9}{9})$

= 2^9 - 1 - 9 - 36

= 512 - 46

=466

The no of polygons with only red vertices is

$(\frac{5}{3} )+ (\frac{5}{4} )+(\frac{5}{5} )$

= 16

The number of convex polygons having at least one blue vertex whose vertices are among the 9 points is

= 466 - 16

= 450

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Know More

1)To find the angle sum of a convex polygon with 9 sides

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2) What will be the angle-sum of a convex polygon with 11 sides?

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