Question

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Answer it ✔✔✔

How many triangles and diagonals can be obtained by joining the vertices of an Octagon ?

Hint -- it can be solved by using Combination . ✔✔✔

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Answer 1

6 Triangles and 40 diagonal can be obtained by joining the vertices of octagon
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Answer 2

Here's the Solution

A triangle can be formed by joining any three vertices of the octagon .

Therefore ,

Number of triangles

= C(8,3)

= 8!/(5!×3!)

=( 8×7×6×5!)/(5!×3×2×1)

= 8×7×6/6

= 56

Again , by joining two vertices we can have a diagonal or line . But we shall also have 8 sides there .

So , Number of diagonals

= C(8,2) - 8

=[ 8!/6!×2! ] - 8

=( 8×7/2 ) - 8

= 28 - 8

= 20